American Express Travel does add fees if you book a flight using its services. If you book through the website, you can expect an additional $6.99 for each domestic ticket and $10.99 for each international ticket. If you make a flight or complete trip reservation by phone, you may be charged a $39 fee per ticket or transaction. Also, if you need to change your flight, Amex may also add a $39 fee to re-issue each ticket. This is in addition to any change fees the airline might charge.