I don't use flash, but here is x-cart's solution...
Code:
{*** Remove this part of code if you want to replace a flash movie with an image ***
<td valign="top">
<object type="application/x-shockwave-flash" data="{$ImagesDir}/custom/flash_logo.swf" width="341" height="206" id="flash_logo" align="top">
<param name="allowScriptAccess" value="sameDomain" />
<param name="movie" value="{$ImagesDir}/custom/flash_logo.swf" />
<param name="menu" value="false" />
<param name="loop" value="false" />
<param name="quality" value="high" />
<param name="bgcolor" value="#ffffff" />
<param name="FlashVars" value="not_home_page={if $main eq "catalog" && $current_category.category eq ""}0{else}1{/if}&final_image={#FinalImage#}&company_name_path={$ImagesDir}/custom/company_name.swf&home_path={$current_location}/customer/home.php" />
<param name="pluginspage" value="http://www.macromedia.com/go/getflashplayer" />
<param name="swLiveConnect" value="true" />
</object>
</td>
*** Remove this part of code if you want to replace a flash movie with an image ***}
It goes in head.tpl in place of where the logo is normally displayed.