The word does not exist.
I hear ”Flügeschlagen“, but that does not make any sense either. The point seems to be that it is a word that sounds German to them American audience, but that they do not understand. A made-up word works fine for that. Few American audience members will be confident enough in their German to be sure that the word does not exist.
On further thought, I could imagine that it was supposed to be “Flügel schlagen” as a joke inside this joke. That would have meant “spread your wings” which maybe would have been meant to indicate that flying would have been the last option left in that situation. However, then somewhere along the line someone would have ruined the joke by messing up the word.