The only three-class AA aircraft are the B772 and B762. Any domestic flight operated by one of these aircraft will have the three-class cabin. There are no three-class B763 -- AA has converted them into a two-class product (all have J/Y).
American's only remaining three class aircraft are 767-200s and 777-200s. On LAX/SFO-JFK routes, AA sells tickets in all three classes. I'm pretty sure any other routes in the system that use 762s or 777s ( DFW-ORD, LAX-ORD, DFW-LAX) are sold as 2 classes.