XML 72 R64.htm IDEA: XBRL DOCUMENT
v3.26.1

Fair Value Measurement - Schedule of Presents the Key Inputs Applied in the Valuations (Details) - Valuation Technique, Black-Scholes-Merton Model [Member] - USD ($) $ / shares in Units, shares in Thousands, $ in Thousands | 3 Months Ended | 12 Months Ended
--- | --- | ---
Mar. 31, 2026 | Dec. 31, 2025
Business Combination [Line Items] |  |
Number of units | 646 | 646
Value of RPM Option | $ 15,978 | $ 12,294
Minimum [Member] |  |
Business Combination [Line Items] |  |
Risk-free rate | 4.09% | 3.94%
Volatility | 94.00% | 92.50%
Term (years) | 7 years 3 months 18 days | 7 years 6 months 18 days
Black-Scholes value (per share) | $ 24.7 | $ 19
Maximum [Member] |  |
Business Combination [Line Items] |  |
Risk-free rate | 4.14% | 4.01%
Volatility | 99.00% | 97.50%
Term (years) | 8 years 1 month 20 days | 8 years 4 months 20 days
Black-Scholes value (per share) | $ 24.8 | $ 19.06
Series J Warrant [Member] |  |
Business Combination [Line Items] |  |
Contractual purchase price for Series J Preferred Stock (per share) | 21.17 | 21.17
Common Stock [Member] |  |
Business Combination [Line Items] |  |
Common Stock Price | $ 28.47 | $ 22.37

X
- Definition Share Based Compensation Arrangement Option Fair Value Assumption + References No definition available. + Details
Name: | fly_ShareBasedCompensationArrangementOptionFairValueAssumption
Namespace Prefix: | fly_
Data Type: | dtr-types:perShareItemType
Balance Type: | na
Period Type: | instant

X
- Definition Share Based Compensation Arrangement Option Outstanding Fair Value + References No definition available. + Details
Name: | fly_ShareBasedCompensationArrangementOptionOutstandingFairValue
Namespace Prefix: | fly_
Data Type: | xbrli:monetaryItemType
Balance Type: | credit
Period Type: | instant

X
- Definition Share Based Compensation Arrangement Option Outstanding Number + References No definition available. + Details
Name: | fly_ShareBasedCompensationArrangementOptionOutstandingNumber
Namespace Prefix: | fly_
Data Type: | xbrli:sharesItemType
Balance Type: | na
Period Type: | instant

X
- Definition Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Topic 350 -SubTopic 20 -Name Accounting Standards Codification -Section 50 -Paragraph 4 -Subparagraph (a) -Publisher FASB -URI https://asc.fasb.org/1943274/2147482573/350-20-50-4 Reference 2: http://www.xbrl.org/2003/role/exampleRef -Topic 805 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 8 -Publisher FASB -URI https://asc.fasb.org/1943274/2147479328/805-10-50-8 Reference 3: http://www.xbrl.org/2003/role/exampleRef -Topic 805 -SubTopic 10 -Name Accounting Standards Codification -Section 55 -Paragraph 47 -Publisher FASB -URI https://asc.fasb.org/1943274/2147479303/805-10-55-47 Reference 4: http://www.xbrl.org/2003/role/disclosureRef -Topic 805 -SubTopic 20 -Name Accounting Standards Codification -Section 50 -Paragraph 5 -Subparagraph (a) -Publisher FASB -URI https://asc.fasb.org/1943274/2147479907/805-20-50-5 Reference 5: http://www.xbrl.org/2003/role/disclosureRef -Topic 805 -SubTopic 30 -Name Accounting Standards Codification -Section 50 -Paragraph 1 -Subparagraph (f)(1) -Publisher FASB -URI https://asc.fasb.org/1943274/2147479581/805-30-50-1 Reference 6: http://www.xbrl.org/2003/role/disclosureRef -Topic 805 -SubTopic 20 -Name Accounting Standards Codification -Section 50 -Paragraph 1 -Subparagraph (d)(1)(i) -Publisher FASB -URI https://asc.fasb.org/1943274/2147479907/805-20-50-1 Reference 7: http://www.xbrl.org/2003/role/disclosureRef -Topic 805 -SubTopic 20 -Name Accounting Standards Codification -Section 50 -Paragraph 1 -Subparagraph (d)(1)(ii) -Publisher FASB -URI https://asc.fasb.org/1943274/2147479907/805-20-50-1 Reference 8: http://www.xbrl.org/2003/role/disclosureRef -Topic 805 -SubTopic 30 -Name Accounting Standards Codification -Section 50 -Paragraph 1 -Subparagraph (b)(3) -Publisher FASB -URI https://asc.fasb.org/1943274/2147479581/805-30-50-1 Reference 9: http://www.xbrl.org/2003/role/disclosureRef -Topic 805 -SubTopic 30 -Name Accounting Standards Codification -Section 50 -Paragraph 1 -Subparagraph (b)(1) -Publisher FASB -URI https://asc.fasb.org/1943274/2147479581/805-30-50-1 Reference 10: http://www.xbrl.org/2009/role/commonPracticeRef -Topic 805 -SubTopic 20 -Name Accounting Standards Codification -Section 50 -Paragraph 1 -Subparagraph (d) -Publisher FASB -URI https://asc.fasb.org/1943274/2147479907/805-20-50-1 Reference 11: http://www.xbrl.org/2003/role/disclosureRef -Topic 805 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (d) -Publisher FASB -URI https://asc.fasb.org/1943274/2147479328/805-10-50-2 Reference 12: http://www.xbrl.org/2003/role/disclosureRef -Topic 805 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (a) -Publisher FASB -URI https://asc.fasb.org/1943274/2147479328/805-10-50-2 Reference 13: http://www.xbrl.org/2003/role/disclosureRef -Topic 805 -SubTopic 20 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Publisher FASB -URI https://asc.fasb.org/1943274/2147479907/805-20-50-2 Reference 14: http://www.xbrl.org/2003/role/disclosureRef -Topic 805 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (c) -Publisher FASB -URI https://asc.fasb.org/1943274/2147479328/805-10-50-2 Reference 15: http://www.xbrl.org/2003/role/disclosureRef -Topic 805 -SubTopic 30 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Publisher FASB -URI https://asc.fasb.org/1943274/2147479581/805-30-50-2 Reference 16: http://www.xbrl.org/2003/role/disclosureRef -Topic 805 -SubTopic 30 -Name Accounting Standards Codification -Section 50 -Paragraph 1 -Subparagraph (a) -Publisher FASB -URI https://asc.fasb.org/1943274/2147479581/805-30-50-1 Reference 17: http://www.xbrl.org/2003/role/disclosureRef -Topic 805 -SubTopic 30 -Name Accounting Standards Codification -Section 50 -Paragraph 1 -Subparagraph (f)(2) -Publisher FASB -URI https://asc.fasb.org/1943274/2147479581/805-30-50-1 Reference 18: http://www.xbrl.org/2003/role/disclosureRef -Topic 805 -SubTopic 20 -Name Accounting Standards Codification -Section 50 -Paragraph 1 -Subparagraph (e)(1) -Publisher FASB -URI https://asc.fasb.org/1943274/2147479907/805-20-50-1 Reference 19: http://www.xbrl.org/2003/role/disclosureRef -Topic 805 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 3 -Publisher FASB -URI https://asc.fasb.org/1943274/2147479328/805-10-50-3 Reference 20: http://www.xbrl.org/2003/role/disclosureRef -Topic 805 -SubTopic 20 -Name Accounting Standards Codification -Section 50 -Paragraph 4A -Subparagraph (c) -Publisher FASB -URI https://asc.fasb.org/1943274/2147479907/805-20-50-4A Reference 21: http://www.xbrl.org/2003/role/disclosureRef -Topic 805 -SubTopic 20 -Name Accounting Standards Codification -Section 50 -Paragraph 4 -Publisher FASB -URI https://asc.fasb.org/1943274/2147479907/805-20-50-4 Reference 22: http://www.xbrl.org/2009/role/commonPracticeRef -Topic 805 -SubTopic 20 -Name Accounting Standards Codification -Section 50 -Paragraph 1 -Subparagraph (b) -Publisher FASB -URI https://asc.fasb.org/1943274/2147479907/805-20-50-1 Reference 23: http://www.xbrl.org/2003/role/disclosureRef -Topic 805 -SubTopic 20 -Name Accounting Standards Codification -Section 50 -Paragraph 1 -Subparagraph (b)(1) -Publisher FASB -URI https://asc.fasb.org/1943274/2147479907/805-20-50-1 Reference 24: http://www.xbrl.org/2003/role/disclosureRef -Topic 805 -SubTopic 20 -Name Accounting Standards Codification -Section 50 -Paragraph 1 -Subparagraph (b)(3) -Publisher FASB -URI https://asc.fasb.org/1943274/2147479907/805-20-50-1 Reference 25: http://www.xbrl.org/2003/role/disclosureRef -Topic 805 -SubTopic 20 -Name Accounting Standards Codification -Section 50 -Paragraph 4A -Subparagraph (b) -Publisher FASB -URI https://asc.fasb.org/1943274/2147479907/805-20-50-4A Reference 26: http://www.xbrl.org/2003/role/disclosureRef -Topic 805 -SubTopic 20 -Name Accounting Standards Codification -Section 50 -Paragraph 1 -Subparagraph (a)(3) -Publisher FASB -URI https://asc.fasb.org/1943274/2147479907/805-20-50-1 Reference 27: http://www.xbrl.org/2003/role/disclosureRef -Topic 805 -SubTopic 20 -Name Accounting Standards Codification -Section 50 -Paragraph 1 -Subparagraph (a)(2) -Publisher FASB -URI https://asc.fasb.org/1943274/2147479907/805-20-50-1 Reference 28: http://www.xbrl.org/2003/role/disclosureRef -Topic 805 -SubTopic 20 -Name Accounting Standards Codification -Section 50 -Paragraph 4A -Subparagraph (a) -Publisher FASB -URI https://asc.fasb.org/1943274/2147479907/805-20-50-4A Reference 29: http://www.xbrl.org/2003/role/disclosureRef -Topic 805 -SubTopic 30 -Name Accounting Standards Codification -Section 50 -Paragraph 4 -Subparagraph (b) -Publisher FASB -URI https://asc.fasb.org/1943274/2147479581/805-30-50-4 Reference 30: http://www.xbrl.org/2003/role/disclosureRef -Topic 805 -SubTopic 30 -Name Accounting Standards Codification -Section 50 -Paragraph 1 -Subparagraph (b)(4) -Publisher FASB -URI https://asc.fasb.org/1943274/2147479581/805-30-50-1 Reference 31: http://www.xbrl.org/2003/role/disclosureRef -Topic 805 -SubTopic 30 -Name Accounting Standards Codification -Section 50 -Paragraph 1 -Subparagraph (b)(2) -Publisher FASB -URI https://asc.fasb.org/1943274/2147479581/805-30-50-1 Reference 32: http://www.xbrl.org/2003/role/disclosureRef -Topic 805 -SubTopic 30 -Name Accounting Standards Codification -Section 50 -Paragraph 1 -Subparagraph (b) -Publisher FASB -URI https://asc.fasb.org/1943274/2147479581/805-30-50-1 Reference 33: http://www.xbrl.org/2003/role/disclosureRef -Topic 805 -SubTopic 20 -Name Accounting Standards Codification -Section 50 -Paragraph 1 -Subparagraph (e)(2) -Publisher FASB -URI https://asc.fasb.org/1943274/2147479907/805-20-50-1 Reference 34: http://www.xbrl.org/2003/role/disclosureRef -Topic 805 -SubTopic 20 -Name Accounting Standards Codification -Section 50 -Paragraph 1 -Subparagraph (c) -Publisher FASB -URI https://asc.fasb.org/1943274/2147479907/805-20-50-1 Reference 35: http://www.xbrl.org/2003/role/disclosureRef -Topic 805 -SubTopic 20 -Name Accounting Standards Codification -Section 50 -Paragraph 1 -Subparagraph (b)(2) -Publisher FASB -URI https://asc.fasb.org/1943274/2147479907/805-20-50-1 Reference 36: http://www.xbrl.org/2003/role/disclosureRef -Topic 805 -SubTopic 20 -Name Accounting Standards Codification -Section 50 -Paragraph 1 -Subparagraph (a)(1) -Publisher FASB -URI https://asc.fasb.org/1943274/2147479907/805-20-50-1 Reference 37: http://www.xbrl.org/2009/role/commonPracticeRef -Topic 805 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (g) -Publisher FASB -URI https://asc.fasb.org/1943274/2147479328/805-10-50-2 Reference 38: http://www.xbrl.org/2003/role/disclosureRef -Topic 805 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (g)(4) -Publisher FASB -URI https://asc.fasb.org/1943274/2147479328/805-10-50-2 Reference 39: http://www.xbrl.org/2003/role/disclosureRef -Topic 805 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (g)(3) -Publisher FASB -URI https://asc.fasb.org/1943274/2147479328/805-10-50-2 Reference 40: http://www.xbrl.org/2003/role/disclosureRef -Topic 805 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (g)(2) -Publisher FASB -URI https://asc.fasb.org/1943274/2147479328/805-10-50-2 Reference 41: http://www.xbrl.org/2003/role/disclosureRef -Topic 805 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (g)(1) -Publisher FASB -URI https://asc.fasb.org/1943274/2147479328/805-10-50-2 Reference 42: http://www.xbrl.org/2003/role/disclosureRef -Topic 805 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (b) -Publisher FASB -URI https://asc.fasb.org/1943274/2147479328/805-10-50-2 + Details
Name: | us-gaap_BusinessAcquisitionLineItems
Namespace Prefix: | us-gaap_
Data Type: | xbrli:stringItemType
Balance Type: | na
Period Type: | duration

X
- Definition Agreed-upon price for the exchange of the underlying asset relating to the share-based payment award. + References Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef -Topic 718 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (f)(2) -Publisher FASB -URI https://asc.fasb.org/1943274/2147480429/718-10-50-2 + Details
Name: | us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExercisePrice
Namespace Prefix: | us-gaap_
Data Type: | dtr-types:perShareItemType
Balance Type: | na
Period Type: | instant

X
- Definition The estimated measure of the percentage by which a share price is expected to fluctuate during a period. Volatility also may be defined as a probability-weighted measure of the dispersion of returns about the mean. The volatility of a share price is the standard deviation of the continuously compounded rates of return on the share over a specified period. That is the same as the standard deviation of the differences in the natural logarithms of the stock prices plus dividends, if any, over the period. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Topic 718 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (f)(2)(ii) -Publisher FASB -URI https://asc.fasb.org/1943274/2147480429/718-10-50-2 + Details
Name: | us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedVolatilityRate
Namespace Prefix: | us-gaap_
Data Type: | dtr-types:percentItemType
Balance Type: | na
Period Type: | duration

X
- Definition The risk-free interest rate assumption that is used in valuing an option on its own shares. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Topic 718 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (f)(2)(iv) -Publisher FASB -URI https://asc.fasb.org/1943274/2147480429/718-10-50-2 + Details
Name: | us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate
Namespace Prefix: | us-gaap_
Data Type: | dtr-types:percentItemType
Balance Type: | na
Period Type: | duration

X
- Definition Price of a single share of a number of saleable stocks of a company. + References No definition available. + Details
Name: | us-gaap_SharePrice
Namespace Prefix: | us-gaap_
Data Type: | dtr-types:perShareItemType
Balance Type: | na
Period Type: | instant

X
- Definition Expected term of award under share-based payment arrangement, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Topic 718 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (f)(2)(i) -Publisher FASB -URI https://asc.fasb.org/1943274/2147480429/718-10-50-2 + Details
Name: | us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedTerm1
Namespace Prefix: | us-gaap_
Data Type: | xbrli:durationItemType
Balance Type: | na
Period Type: | duration

X
- Details
Name: | us-gaap_ValuationTechniqueAxis=us-gaap_BlackScholesMertonModelMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | srt_RangeAxis=srt_MinimumMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | srt_RangeAxis=srt_MaximumMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | us-gaap_StatementClassOfStockAxis=fly_SeriesJWarrantMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | us-gaap_StatementEquityComponentsAxis=us-gaap_CommonStockMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |