The Fly PETS Act would allow the federal government to use appropriated funds to pay for transporting federal employees' pets when traveling on official business. The bill applies to federal civilian employees, military members, Foreign Service officers, and Peace Corps volunteers who are traveling between the U.S. and foreign countries or between two foreign locations. Under the bill, federal funds could cover pet transportation costs on foreign airlines only when U.S. carriers are unwilling or unable to transport up to three domesticated animals, with pets limited to dogs, cats, or other animals the Secretary of Transportation deems appropriate. Federal employees would be required to pay any difference if the foreign airline's cost exceeds what a U.S. carrier would have charged. The legislation does not establish new funding amounts and instead modifies existing federal travel appropriations to permit this exception to current law requiring federal employees to use U.S. carriers when available.