Flood Insurance Integrity Act of 2019 This bill directs the Government Accountability Office (GAO) to review every four years the rate tables established by the Federal Emergency Management Agency (FEMA) for implementing the National Flood Insurance Program (NFIP). The GAO must determine whether (1) the chargeable premium rates for flood insurance coverage are actuarially sound, based on standard actuarial practices used in the private sector; and (2) such chargeable premium rates are sufficient to ensure the long-term financial sustainability of NFIP. The bill also directs the GAO to review annually the process for establishing and updating flood insurance rate maps and determine the degree of accuracy of the mapping process.