Flight School Security Act of 2013 - Revises requirements with respect to the training of aliens and other individuals designated by the Secretary of Homeland Security (DHS) in the operation of certain aircraft.

Authorizes a flight instructor, pilot school, or aviation training center to provide training in the operation of an aircraft with a takeoff weight of more than 12,500 pounds to an individual who does not hold a valid Federal Aviation Administration (FAA) airman's certification only if: (1) that individual has been checked against the terrorist watchlist by the Assistant Secretary of Homeland Security (Transportation Security Administration [TSA]) to determine if he or she poses a threat to aviation or national security or a threat of terrorism, and (2) the Assistant Secretary determines that the individual does not pose a threat that warrants denial of access to such training.