Well, flash works for me (Gentoo, KDE 3.1.1, flash plugin that
comes with Gentoo). So it's not a fundamental incompatibility
but seems to be a problem with your installation/distro.
But: The page
http://www.transelement.co.uk/
doesn't work for me (right clicking on the solid blue
background shows the typical flash context menu, but it
says "movie not loaded"). In Mozilla it works, though.
AFAIK they're using the same plugin... no idea what
causes the different behaviour.
----
If you manage to get to the "Configure Konqueror"
menu you should check whether the search path list
inlcudes the directory you installed the plugin to.
You might try the control center, too.
All the konqi config menus should be duplicated there, too.
See: Internet & Networking -> Web-Browser