Well, as far as I can tell, your problem lies with the lack of code calling the swf in your header.php file in your theme.
At the moment it reads:
<div id="header">
<div id="headerimg">
<h1><a href="https://www.wellworthdriving.com/"></a></h1>
<div class="description"></div>
</div>
</div>
Which means there’s no way any flash is going to show up.
I suggest you edit your header.php and include the following code in <div id=”header”>:
<object classid="clsid:d27cdb6e-ae6d-11cf-96b8-444553540000" codebase="https://fpdownload.macromedia.com/pub/shockwave/cabs/flash/swflash.cab#version=8,0,0,0" width="enterwidth" height="enterheight" id="flashbanner">
<param name="allowScriptAccess" value="sameDomain" />
<param name="movie" value="<?php bloginfo('stylesheet_directory'); ?>/images/header.swf" />
<param name="wmode" value="transparent" />
<!--[if !IE]>-->
<object type="application/x-shockwave-flash" data="<?php bloginfo('stylesheet_directory'); ?>/images/header.swf" width="enterwidth" height="enterheight">
<param name="movie" value="slideshow.swf" />
<param name="wmode" value="transparent" />
</object>
<!--<![endif]-->
</object>
Hopefully that should do it?