Welcome to FT miwill ^

I think it unlikely as your internal flight will probably go from a different terminal (B, C or D). The BA lounge is airside in Terminal A but if memory serves me correctly all AA flights from there are international.

Also, with a US internal flight I think you have to clear Immigration then Customs on arrival in MIA which will bring you landside.

I think there have been some changes in MIA since I was last there. Maybe another FTer can advise. krug where are you?!