Welcome to FT.
When you are booking the ticket on aa.com, choose the flexible option. Then on the fare grid, you have the flexible and fully flexible. Fully flexible should be completely unrestricted with no fees for refund.
The vast majority of Flexible fares do not have a fee for refund (if there is one, it will be listed in Fare Rules under Penalties section) and there is no need in most cases to upfare to Fully Flexible (which can be substantially more money than Flexible fares) if you just want a fare that is refundable without fees. The primary difference between Flexible and Fully Flexible fares is that Fully Flexible fares do not have advance purchase requirements and can generally be changed up to departure without incurring fare difference charges. If you want to change a Flexible fare (instead of just refunding it), you will often encounter charges for fare differences should you no longer meet original advance purchase requirements for the Flexible fare you purchased.
When it comes to changing flights, booking class availability can also be a factor and you may have to pay fare difference in the event there is no longer fare booking class availability in your originally booked flights in the new flights you are attempting to change to (even if you still meet advance purchase requirements for originally booked fare).