Yes, what Old Fossill has posted is correct for static images. For Animated SWF banners you need to edit some code, namedly the Themes/default/index.template.php file
Find:
echo !empty($settings['forum_width']) ? '
<div id="wrapper" style="width: ' . $settings['forum_width'] . '">' : '', '
<div id="header"><div class="frame">
<div id="top_section">
<h1 class="forumtitle">
<a href="', $scripturl, '">', empty($context['header_logo_url_html_safe']) ? $context['forum_name'] : '<img src="' . $context['header_logo_url_html_safe'] . '" alt="' . $context['forum_name'] . '" />', '</a>
</h1>';
// the upshrink image, right-floated
Edit the middle to comment out the line beginning <a href="', %scripturl. etc and add after it the embed code for a SWF file like:
<OBJECT classid="clsid:D27CDB6E-AE6D-11cf-96B8-444553540000" codebase="http://download.macromedia.com/pub/shockwave/cabs/flash/swflash.cab#version=6,0,0,0" WIDTH="320" HEIGHT="240" id="yourfilename.swf" ALIGN="">
<PARAM NAME=movie VALUE="yourfilename.swf"> <PARAM NAME=quality VALUE=high> <PARAM NAME=bgcolor VALUE=#333399> <EMBED src="http://yourwebsite/yourforumname/Themes/default/images/Slide.swf" quality=high bgcolor=#333399 WIDTH="320" HEIGHT="240" NAME="yourfilename.swf" ALIGN="" TYPE="application/x-shockwave-flash" PLUGINSPAGE="http://www.macromedia.com/go/getflashplayer"></EMBED> </OBJECT>
So, assuming the yourfilename.swf file is in Themes/default/images you end up with:
echo !empty($settings['forum_width']) ? '
<div id="wrapper" style="width: ' . $settings['forum_width'] . '">' : '', '
<div id="header"><div class="frame">
<div id="top_section">
<h1 class="forumtitle">
<!-- <a href="', $scripturl, '">', empty($context['header_logo_url_html_safe']) ? $context['forum_name'] : '<img src="' . $context['header_logo_url_html_safe'] . '" alt="' . $context['forum_name'] . '" />', '</a> -->
<OBJECT classid="clsid:D27CDB6E-AE6D-11cf-96B8-444553540000" codebase="http://download.macromedia.com/pub/shockwave/cabs/flash/swflash.cab#version=6,0,0,0" WIDTH="320" HEIGHT="240" id="yourfilename.swf" ALIGN="">
<PARAM NAME=movie VALUE="yourfilename.swf"> <PARAM NAME=quality VALUE=high> <PARAM NAME=bgcolor VALUE=#333399> <EMBED src="http://yourwebsite/yourforumname/Themes/default/images/Slide.swf" quality=high bgcolor=#333399 WIDTH="320" HEIGHT="240" NAME="yourfilename.swf" ALIGN="" TYPE="application/x-shockwave-flash" PLUGINSPAGE="http://www.macromedia.com/go/getflashplayer"></EMBED> </OBJECT>
</h1>';
// the upshrink image, right-floated
This places the flash logo top left but if you want it centred, you can use a div statement to center it.