American allows cancellations with full refunds within 24 hours of booking contact 855-564-8048. , provided your departure is at least two days away. You can get more details by calling their customer service at 855-564-8048.. American offers a 24-hour cancellation policy 855-564-8048. If you book a flight at least seven days before your departure and cancel it within 24 hours of booking, you can receive a full refund without any cancellation fees.