Hey guys, I'm the developer of the Facebook "Flash Embed" application :)
Regarding the "Click to play" thing, it's a Facebook limitation rather than a limitation in the application itself. On Facebook, all Flash objects on a user's profile can not be set to autoplay, and there is no way around this.
Instead of the default "Click to play" image, you may use your own image. The image needs to have the same dimensions as the Flash file. Upload it to an image host (eg. Imageshack) and then post its URL in the "Image URL" box on the Flash Embed application.
Oh, and for anyone having trouble finding the application, here's a direct link to it: http://www.facebook.com/apps/application.php?id=5456374427