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If the board on which you are posting suports the use of HTML, then yes, it is possible. Just paste the HTML object tag into your sig or post.
This site does not allow HTML in signatures or posts, so you can't do it on XOOPS.org. Every site has different preferences regarding whether they allow HTML in posts or sigs.
Note: It's bad netiquette to put large Flash files in a signature, just so ya know.