I'm building this website where I have an swf file in the root. ZP is installed in root/zenphoto. The swf loads in all root pages, but not on the index.php or album.php file inside the themes folder. I am using relative paths.

does not work: http://www.dewaele-tegelkachels.be/zenphoto/themes/puregraphx/isolatie.php
does work: http://www.dewaele-tegelkachels.be/isolatie.php

This is exactly the same file.

Maybe you should tell a few more info what you are actually trying to do and what this isolatie.php file actually does. The not working link is in any case not a Zenphoto link and therefore not even in Zenphoto context. I suggest to read the theming tutorial.

The problem is with the flash file which loads on the one page but not on the other, even though those 2 pages are identical. It's like a relative link to "/header_flash.swf" inside a ZP album.php page doesn't seem to get "out" of the ZP root, to reach the main website root.

Since you installed Zenphoto in a folder "zenphoto" /header_flash.swf of course does not reach your website root as that would be the root of the Zenphoto install naturally...