You need to properly reference the *.swf file. My guess is, you refer to your *.swf file in realtive terms, something like this:
<object type="application/x-shockwave-flash" data="menu.swf">
The problem is, your template code will be included into the blog's main index file, so all relative references will be perceived as relative to the blog's home directory. So, if my guess is correct, you can fix the problem by providing an absolute link to the *.swf file.
If your *.swf file is stored in the same directory as the template file, you can do it like this:
<object type="application/x-shockwave-flash" data="<?php
bloginfo('template_directory');
?>menu.swf">
I can't remember if bloginfo('template_directory') returns the directory with or without a trailing slash. The example above assumes it is with a trailing slash. If not, just add a slash manually, so that ?>menu.swf"> becomes ?>/menu.swf">...