Perhaps the question you should be asking is: " Is it possible to embed Flash in Processing?"

And tbh I think the valid response: is why on earth would you want to?  They both do more or less the same thing: ActionScript can be converted to Processing easily enough (and vice versa).  Of course you don't have the luxury of a MovieClip class in Processing and all those animation features out of the box...  but I certainly haven't had too many problems converting between the two.

Blindfish, what program or process do you use to convert Processing to Flash and vice versa.

I agree that Processing is better than Flash but I do see .swf files that would look great in Processing.
Basically anything in Processing would be suitable for Flash (for demonstration purposes)

You could integrate the native browser into a Processing sketch, which would then support whatever the browser supports to include flash.  I had some tests going with DJNativeSwing and Lobo.  I was thinking of embedding the browser into an existing sketch with the napplet library but never got around to it.

I don't use Processing as an applet, so I wouldn't know.  I export all my sketches as an application, so I'm essentially just running a java program with an embedded browser.