We have J tickets acquired via mileage redemption from LAX to South America. I haven't been able to figure out if these get us Flagship Lounge - a cash purchase would have been labeled as a Flagship flight, but I am not sure about mileage tickets as it doesn't reference Flagship. Our outbound flight has a stop at JFK and our inbound stops in DFW. If it doesn't get us Flagship, does it get us the minimal Admirals club? Thanks so much!
AA is horribly inconsistent with its "Flagship" marketing. Any long haul flight in business class = Flagship regardless of whether it's paid or award or what is displayed at aa.com.
So assuming your flights to South America are to/from a qualifying country (i.e. not Northern SA) you will have no problem accessing the Flagship Lounges at LAX, JFK, and DFW during your trip.