Transit Security Grant Program Flexibility Act This bill establishes periods of performance for the use of public transportation security assistance grant funds. Additionally, the bill allows such grants provided for operational purposes to be used to backfill positions when employees attend security training. Funds provided pursuant to such a grant for a specified authorized use, including for tunnel protection systems and surveillance equipment, shall remain available for use by a grant recipient for at least 36 months. However, any such funds used for security improvements for public transportation systems or security improvements for stations and other public transportation infrastructure, including those owned by state or local governments, shall remain available for at least 55 months. The Government Accountability Office shall conduct a review of the public transportation security assistance grant program, including an assessment of the manner in which projects under the program address threats to public transportation infrastructure.