It's not a bad idea on paper, but the difference between BA's F lounges and AA's F lounges are night and day. In fact, at LHR (the only place that readily comes to mind with a sizable AC and FL on the AA size, and sizable Galleries First and Club on the BA side), I would probably prefer BA Galleries Club to AA Flagship Lounge if I were forced to choose. BA and AA have proven their interest in working together at smaller stations with no BA F service (DEN), but I can't see BA being happy with AA's level of F lounge for their passengers. Operating separate lounges allows BA and AA to offer their passengers the level of service they want to offer, and since only a portion of AA's frequent flyers know that they can use the BA lounge on qualifying international itineraries, AA won't have to offer everyone the BA level of service. Just my two pence.