Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

Flushing Bank 401(k) Savings Plan

Uniondale, NY

We hereby consent to the incorporation by reference in the Registration Statement on Form
S-8 (33-98202, 333-151187, 333-163010, 333-188776, 333-219707) of Flushing Financial Corporation of our report dated June 23, 2020, relating to the financial statements and supplemental schedule of Flushing Bank 401(k) Savings Plan which appear in this Form 11-K for the year ended December 31, 2019.

BDO USA, LLP

New York, NY

June 23, 2020