I'll be departing from LHR nonstop to AUS this July in Club World on BA via a reward ticket I recently obtained using my AAdvantage miles. From AUS, I'll will be connecting on the same day to DFW in F on AA with an additional same day connection at DFW on to LFT on AA Eagle in F.

Question: Will I be able to use the Admirals Club at AUS as well as the Flagship Lounge at DFW in view of my LHR-AUS-DFW-LFT itinerary in business on BA and first on AA taking place on the same date?