Basically Mike Koval's answer will do the job, that is setting wmode="transparent"
. All other HTML/CSS/JS things will remain the same from your own link.
Full embedding code HTML version (by swfObject's generator) will be:
<object classid="clsid:D27CDB6E-AE6D-11cf-96B8-444553540000" width="800" height="600" id="myFlashContent">
<param name="movie" value="path/to/flash.swf" />
<param name="wmode" value="transparent" />
<!--[if !IE]>-->
<object type="application/x-shockwave-flash" data="path/to/flash.swf" width="800" height="600">
<param name="wmode" value="transparent" />
<!--<![endif]-->
<a href="http://www.adobe.com/go/getflashplayer">
<img src="http://www.adobe.com/images/shared/download_buttons/get_flash_player.gif" alt="Get Adobe Flash player" />
</a>
<!--[if !IE]>-->
</object>
<!--<![endif]-->
</object>
It will be always better to use swfObject in JS, something like:
var flashvars = {};
var params = {};
params.wmode = "transparent";
var attributes = {};
swfobject.embedSWF("path/to/flash.swf", "id-of-the-div-the-flash-will-go", "800", "600", "9.0.0", false, flashvars, params, attributes);