Adobe are going to (it seems) announce AIR on mobiles, and Flash Player 10 (though confusingly, they just seem to want to just call it Flash Player...) on mobiles at MAX 2009 in October.
I wouldn't expect to see anything actually hitting mobiles until early 2010.
The demo of the HTC Hero phone appears to show Flex apps running in web pages, but the accompanying blurb suggests the AVM is looking for AS2 rather than AS3, so it doesn't even appear that is good enough yet.
Short answer (after making you read all that ) : Wait until next year.
It has been announced that Palm Pre will suppot Flash Player 10 before end of year; so if your Max 09 suspicion is correct, I'd expect it to be available immedately at the announcement.
That said, I haven't heard any speculation on Flash Player 10 for Mobile or AIR for Mobile coming out at Max. I've actually heard very little about "AIR Mobile" at all.
Got any sources?
Some blog speculation and the published sessions for MAX 09...
Looks like it isn't particularily imminent (the sessions on AIR on the mobile are previews) but it looks like a reality.