Flexibility to Promote Reemployment Act This bill authorizes the Department of Labor to enter into agreements with 10 states per year (currently, 10 states total) for the purpose of allowing such states to conduct reemployment demonstration projects. In addition to a governor of a state, a designee of a governor may apply for approval of such a project. The allowable project period is extended through December 31, 2021. A demonstration project may include disbursements promoting retention to employers who hire individuals receiving unemployment compensation. Labor must approve completed applications in the order of receipt. Labor may terminate a demonstration project under this bill if it notifies the state in writing with sufficient detail describing the violation and determines that the state has not taken action to correct the violation within 90 days after the notification. The bill directs Labor to evaluate the impact of each demonstration project using existing data sources and methodology appropriate to determine project effects, including the effect on individual skill levels, earnings, and employment retention.