The Flagship Lounges are physically separate from the Admirals Club (although some locations, like the new DFW Lounge its a separate lounge within the Admirals Club).
Admirals Clubs serve complimentary soft drinks and juices, varying snack mixes and sometimes cheese and crackers. There is (usually, see below) a charge for alcohol.
Membership, or being the guest of a member, is usually required for Admirals Club access. International first and business class passengers are admitted on the dates of travel. When travelling internationally in first or business you should be offered at least two complimentary drink coupons per adult. Some agents have said to simply ask if more are required.
Flagship Lounges are intended for transoceanic international first class passengers and the elite status passengers discussed in previous posts. In my opnion, the Flagship Lounges are nicer and more comfortable that Admirals Clubs. In addition, all beverages are complimentary. Hot and cold buffet food and desserts are also available; depending upon how much you consume it could be considered a meal. Examples I've experienced include shrimp, sausages, meatballs, chicken/beef skewers and sushi in the U. S., quiche, finger sandwiches, etc. in London.