It certainly is possible but probably not how you are thinking.
The best approach is to create a static index page that offers links to 1) a flash version and 2) a staic html version of your site.
The spiders will crawl your html site and some of your visitors will enjoy your flash version. Also don't forget that some of your visitors will not have a fast connection to the inet and the flash version will be painful for them causing many to leave before giving you a chance.
Keep in mind that the main objective of most Sites is to sell products or services. If your potential clients cannot find your site because it can't be indexed by the SE's (flash) or if they can't get to your products or services very quickly because of a bandwidth heavy flash animation and a slow connection speed...well, your business is going to suffer