Exhibit 5.1

Sean M. Clayton

T: +1 858 550 6034

sclayton@cooley.com

December 8, 2014

Flexion Therapeutics, Inc.

10 Mall Road, Suite 301

Burlington, MA 01803

Ladies and Gentlemen:

We represent Flexion Therapeutics, Inc., a Delaware corporation (the “Company”), in connection with the filing by the Company of a Registration Statement (No. 333-200668) on Form S-1 (the “Registration Statement”) with the Securities and Exchange Commission, including a related prospectus filed with the Registration Statement (the “Prospectus”), covering an underwritten public offering of up to 4,025,000 shares (the “Shares”) of the Company’s common stock, par value $0.001, which includes up to 3,500,000 Shares to be sold by the Company (the “Company Shares”) and up to 525,000 Shares of common stock of the Company that may be sold by the Company pursuant to the exercise of an of an over-allotment option granted to the underwriters (the “Overallotment Shares”).

In connection with this opinion, we have examined and relied upon (a) the Registration Statement and related Prospectus, (b) the Company’s Amended and Restated Certificate of Incorporation and Amended and Restated Bylaws, as currently in effect and (c) the originals or copies certified to our satisfaction of such records, documents, certificates, memoranda and other instruments as in our judgment are necessary or appropriate to enable us to render the opinion expressed below. We have assumed the genuineness and authenticity of all documents submitted to us as originals and the conformity to originals of all documents submitted to us as copies. As to certain factual matters, we have relied upon a certificate of an officer of the Company and have not sought independently to verify such matters. Our opinion is expressed only with respect to the General Corporation Law of the State of Delaware. We express no opinion as to whether the laws of any particular jurisdiction are applicable to the subject matter hereof. We are not rendering any opinion as to compliance with any federal or state antifraud law, rule or regulation relating to securities, or to the sale or issuance thereof.

On the basis of the foregoing, and in reliance thereon, we are of the opinion that the Company Shares and the Overallotment Shares, when sold and issued against payment therefor as described in the Registration Statement and the related Prospectus, will be validly issued, fully paid and non-assessable.

4401 Eastgate Mall, San Diego, CA 92121 T: (858) 550-6000 F: (858) 550-6420 www.cooley.com

Flexion Therapeutics, Inc.

December 8, 2014

Page Two

We consent to the reference to our firm under the caption “Legal Matters” in the Prospectus included in the Registration Statement and to the filing of this opinion as an exhibit to the Registration Statement.

4401 Eastgate Mall, San Diego, CA 92121 T: (858) 550-6000 F: (858) 550-6420 www.cooley.com