By default, the chat window is behind the Flash movie in the webpage.
So, you may need to insert the HTML Code in the flash code for upper on the Flash movie.

You should insert this HTML code in to the flash movie code area:
<param name="WMODE" value="transparent">

For example:

<object classid="clsid:D27CDB6E-xxxx-11cf-96B8-444xxxxx0000" codebase="http://download.macromedia.com/pub/shockwave/cabs/flash/swflash.cab#version=6,0,29,0" width="491" height="126">
<param name="movie" value="../images/index_banner.swf">
<param name="WMODE" value="transparent">
<param name="quality" value="high">
<embed src="../images/index_banner.swf" quality="high" pluginspage="http://www.macromedia.com/go/getflashplayer" type="application/x-shockwave-flash" width="491" height="126"></embed>
</object>