Exhibit 5.1

1221 PEACHTREE STREET, N.E. • SUITE 400 • ATLANTA, GEORGIA 30361

TELEPHONE: +1.404.521.3939 • JONESDAY.COM

February 14, 2025

Flowers Foods, Inc.

1919 Flowers Circle

Thomasville, Georgia 31757

Re: $500,000,000 of 5.750% Senior Notes due 2035 and

$300,000,000 of 6.200% Senior Notes due 2055

of Flowers Foods, Inc.

Ladies and Gentlemen:

We are acting as counsel for Flowers Foods, Inc., a Georgia corporation (the “Company”), in connection with the issuance and sale of (i) $500,000,000 aggregate principal amount of the Company’s 5.750% Senior Notes due 2035 (the “2035 Notes”) and (ii) $300,000,000 aggregate principal amount of the Company’s 6.200% Senior Notes due 2055 (together with the 2035 Notes, the “Notes”), pursuant to the Underwriting Agreement, dated February 11, 2025, by and among the Company and BofA Securities, Inc., Deutsche Bank Securities Inc., RBC Capital Markets, LLC, and Wells Fargo Securities, LLC, acting as representatives of the several underwriters named therein. The Notes are being issued under the Indenture, dated as of April 3, 2012 (the “Base Indenture”), by and between the Company and Computershare Trust Company, N.A. (as successor to Wells Fargo Bank, National Association), as trustee (the “Base Indenture Trustee”), as amended and supplemented from time to time, including without limitation, pursuant to the Officer’s Certificate, dated February 14, 2025 (the “Officer’s Certificate” and, together with the Base Indenture, the “Indenture”), establishing the specific terms and forms of the Notes, each as a new series of securities under the Indenture, and appointing Regions Bank to serve as series trustee with respect to the Notes (the “Series Trustee”).

In connection with the opinion expressed herein, we have examined such documents, records and matters of law as we have deemed relevant or necessary for purposes of this opinion. Based on the foregoing, and subject to the further limitations, qualifications and assumptions set forth herein, we are of the opinion that the Notes constitute valid and binding obligations of the Company.

For purposes of the opinion expressed herein, we have assumed that (i) the Base Indenture Trustee has authorized, executed, and delivered the Base Indenture, (ii) the Series Trustee has authorized, executed and delivered the Officer’s Certificate, (iii) the Notes have been duly authenticated by the Series Trustee in accordance with the Indenture, and (iv) each of the Base Indenture and the Officer’s Certificate is the valid, binding and enforceable obligation of the Base Indenture Trustee or the Series Trustee, as applicable.

AMSTERDAM • ATLANTA • BEIJING • BOSTON • BRISBANE • BRUSSELS • CHICAGO • CLEVELAND • COLUMBUS • DALLAS

DETROIT • DUBAI • DÜSSELDORF • FRANKFURT • HONG KONG • HOUSTON • IRVINE • LONDON • LOS ANGELES • MADRID

MELBOURNE • MEXICO CITY • MIAMI • MILAN • MINNEAPOLIS • MUNICH • NEW YORK • PARIS • PERTH • PITTSBURGH

SAN DIEGO • SAN FRANCISCO • SÃO PAULO • SHANGHAI • SILICON VALLEY • SINGAPORE • SYDNEY • TAIPEI • TOKYO • WASHINGTON

Flowers Foods, Inc. February 14, 2025 Page 2

The opinion expressed herein is limited by: (i) bankruptcy, insolvency, reorganization, fraudulent transfer and fraudulent conveyance, voidable preference, moratorium or other similar laws and related regulations and judicial doctrines from time to time in effect relating to or affecting creditors’ rights generally, and (ii) by general equitable principles and public policy considerations, whether such principles and considerations are considered in a proceeding at law or at equity.

As to facts material to the opinion and assumptions expressed herein, we have relied upon oral and written statements and representations of officers and other representatives of the Company and others. The opinion expressed herein is limited to the laws of the State of New York and the laws of the State of Georgia, in each case as currently in effect, and we express no opinion as to the effect of the laws of any other jurisdiction.

We hereby consent to the filing of this opinion as Exhibit 5.1 to the Current Report on Form 8-K dated the date hereof filed by the Company and incorporated by reference into the Registration Statement on Form S-3 (Reg. No. 333-274116) (the “Registration Statement”), filed by the Company to effect the registration of the Notes under the Securities Act of 1933 (the “Act”) and to the reference to Jones Day under the caption “Legal Matters” in the prospectus constituting a part of such Registration Statement. In giving such consent, we do not hereby admit that we are included in the category of persons whose consent is required under Section 7 of the Act or the rules and regulations of the Securities and Exchange Commission promulgated thereunder.

Very truly yours,

/s/ Jones Day