I’ve only accomplished it via the header.php file, not the style sheet.
<object classid="clsid:D27CDB6E-AE6D-11cf-96B8-444553540000" codebase="https://download.macromedia.com/pub/shockwave/cabs/flash/swflash.cab#version=6,0,29,0" width="719" height="47">
<param name="movie" value="https://www.yoursite.com/flash/header.swf">
<param name="quality" value="high">
<embed src="https://www.yoursite.com/flash/header.swf" quality="high" pluginspage="https://www.macromedia.com/go/getflashplayer" type="application/x-shockwave-flash" width="719" height="47"></embed></object>
Make sure your path is correct in both places. I’m not a flash designer, so there may be other options, this is simply the manner in which I was able to accomplish it.
Obviously you’ll adjust the width and height to the size of your flash as well, and adjust any file names.