I question why you think it'd "improve the user experience" if your logo were animated. Animation on a web page is usually a distraction, not an improvement. Mind you, there are exceptions to any rule but you really need to be sure that animation will be a true improvement and not just another whiz-bang feature that doesn't provide anything in the way of actual content.
Likewise, unless you're displaying your logo full sized as the major content on a page, Flash is the wrong technology. A simpler animated GIF file would be a better choice.
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