I want to listen to the audio portion of flash on my Droid preferably with the screen off. Sites like InfoQ.com have great interviews in flash that I want to just listen to.
This is an old question, but there just might be an answer which someone might benefit from.
Take a look at Uz Media Player https://play.google.com/store/apps/details?id=net.uzumaki.android.mediaplayer
This may be a silly thing to say, but have you tried loading a site with flash, and letting it play? I would have thought it would just continue even if the screen goes blank.
If it does stop when the screen goes blank, can you download it and play it using one of the audio players that supports .flv and has the option to continue playing in the backgound? Is there an app that can play .flv?
Regarding playing non-MP4 or H.264:
Here's a SO question about having trouble stopping flash when leaving the browser.