Paycheck Protection Program Loan Forgiveness Flexibility Act of 2021 This bill modifies the rehiring deadline by which a participant in the Paycheck Protection Program, established to support small businesses in response to COVID-19 (i.e., coronavirus disease 2019), must return to pre-pandemic levels of employment in order to be eligible for loan forgiveness. Specifically, the bill sets this rehiring deadline to 90 days after the termination of all state and local COVID-19 emergency declarations that apply to the location of the recipient.