I understand your point regarding the term Flame Out. My understanding of this term is its a situation where a Turbine Engine fails to continue operation due to inability to maintain flame propagation through any of a number of extinguishing events. Off the top of my head these would include: Compressor Stalls, Insufficient Airflow, Mass Water Ingestion and or Contaminated Fuel Supply. Basically anything other than a mechanical failure of the Power Plant; which would be classified as an Engine Failure.
Notice I have avoided the use of the term Engine Shutdown which would include Flight Crew operation of normal Fuel Shutoff procedures, Fire T-Handle applications and arguably Running Out of Fuel. I have never stated that the Flight Crew of U.S. Airways Flight 1549 Shutdown the Engines. Once again, my point was simply if the Flight Crew had the APU fully available at the time both engines ceased operations, would that possibly have had an impact on the situation? Specifically, provide instant Pneumatic resources to attempt a restart?
I raise this question because I feel it could have been a factor in this event. Pre-fuel conservation flight ops would not have the APU shutdown before Take off. This current procedure of shutting off the APU after Engine(s) start & restarting upon taxi-in are typical of most Operator's Fuel Saving Programs.