Families Flying Together Act of 2013 - Directs the Secretary of Transportation (DOT) to issue regulations directing each air carrier to: (1) establish a policy to ensure that a family that purchases tickets for a flight is seated together during that flight, and (2) make the policy available to the public on the air carrier's website.

Defines "family" to mean a grouping of individuals that, at a minimum, includes: (1) a child age 12 years or younger; and (2) an individual age 18 years or older and responsible for accompanying that child, including a parent or legal guardian of that child.