For General Aviation Aircraft the pilots are required to demonstrate emergency procedures for multi Engine aircraft as well as emergency procedures for gear extension and the like. They don’t do any type of training for wing damage or lose of controls.
The airlines do a lot using simulators and can configure to simulate most any type of problem that they either have experienced or have seen others experience. Every flight officer in every airline has had it drilled into their heads the escape maneuver for a micro burst down draft associated with thunderstorms. And using deferential power to steer with multiple malfunctions of elevator.
But with most commercial airlines cockpit procedures are for shutting down systems or overriding systems or restarting systems and following checklists and procedures. That all takes time and as we saw sometimes there just isn’t enough time to complete the entire procedure that 757 in the Hudson was a good example. The air restart check list takes about 3 minutes to run through for each engine.
For what the military might train for is not much different then the airlines. Mostly systems shut down and start up. If they have a malfunction that causes them a lost of control. They punch out. When it goes bad it goes bad fast. The number of aircrews that become POW’s in any war zone is testimony to that fact. Aircraft just don’t fly very well all shot up and missing parts. Yes, there are pictures of B17 missing the outer wings and tails and still returning, but consider that an unusual event. Most B17’s with lose of control services spin in. Very few fighters would have fared as well. Modern aircraft such as the 30 year old A10, (warthog) appear to have been blessed with some of the B17’s rugged survival skills. But the training for the pilots is if you lose control , get out.
The relight procedure doesn't have to take 3 minutes. Jet engines are very simple to start. Most take less than a minute to start.
The question is whether or not you can get the conditions necessary for a relight. Most of the time they relight on their own after a flameout. You need sufficient rotation, fuel and ignition. A dual flame out at low altitude means the engines spool down very quickly and need increased airspeed or an alternate bleed air source to spin the engine into start parameters (unless it is a fairly small jet engine and uses electric starter motors).
I had a pilot induced double flame out in a Lear 60 once. The pilot shut down the wrong engine during an engine failure at about 500 feet above the ground. The engine was spooling back up through 65% when we hit the ground about 40 seconds later.
