In another thread (why make a new one?), I advised to search Java libraries to do this. Have you done this?

To my knowledge, there is no simple way to do that.
Now, there are convoluted ways...
The "simplest" way is probably to find and use a Java library embedding a native browser component (IE's one or Gecko, Firefox' one) so it can display HTML and embedded Flash components.
Not a small task...

this example show how to render proper HTML from inside Processing.
not sure though if it supports flash.

http://workshop.evolutionzone.com/2007/08/30/jdic-embedding-a-web-browser-in-java/