There are veterans and seniors as well as for some students discounts, but you won't find codes anywhere. What you see on their website is what they offer and I don't know anything about
AAA, but I didnt' see it listed on Amtrak. I do know that some discounts do not apply to the Auto Train. The best way to find out is to go to the Amtrak site and plan a trip. It will tell you what it will cost you based on what you put in. How far out and in what season you book will make the cost vary as will your type of accomodations.