Do you mean create flash content, or merely view it on the internet? If the latter, then there already exists a flash plugin for Linux.
As for other Adobe products, the list is quite short. There is a native version of Adobe Reader, but that's it as far as I'm aware.
If you want to use a native Linux app that is like Photoshop, there's the GIMP (which is available for Windows too, so you could try before you buy, so to speak). Otherwise, if you're dead set on using Photoshop, I believe it runs pretty well under "wine", which is a program which provides an alternative Windows' API, allowing native Windows applications to run on Linux. See their AppDB for more info:
http://appdb.winehq.org/, specifically
http://appdb.winehq.org/appbrowse.php?catId=19 should get you started.
