American Airlines Booking Phone Number Arlington Airport - Passengers flying with American Airlines from Arlington area airports can easily manage their bookings through the official booking phone number. With just one call, you can book new tickets, confirm existing bookings, change flight schedules, cancel trips or request a refund. Passengers can also use this number to get updates on flight times, check-in options, seat upgrades and premium class bookings. For a quick and reliable travel experience, dial the American Airlines booking phone number Arlington Airport today and book your trip.