Palm OS handhelds never ever supported flash, and are unlikely to get Flash support now. However, other handsets might just be in luck – the slide below is from an Adobe keynote:

As of now, nobody knows which devices will be affected – but things nevertheless could get very interesting soon…
The full slide deck can be had here:
http://www.adobe.com/aboutadobe/invrelations/09q2analyst/
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Hmmm… Wasn’t there a model of the Sony Clie that ran Palm OS and had a version of Flash?
Yes the Sony Clies (TG-50, TH-55) with OS 5 had the capability to play the early versions of Flash. On Treo Central someone was able to port the program for a Treo 650 and Flash was able to play on some Treos.