Flagship First Dining is sort of a super-premium product, but not exactly a "lounge" as we use that word. So the normal admission rules don't apply. I couldn't get the link in remdk's post to work for me; but here's a link to the AA page with details. Link. The way that it seems to be worded, admission may be available only to AA F pax and even then only on certain flights. Best to call AA to be sure.