some websites don't work with flash, others do. same with java. so it might simply be the webpage (or koqueror) at fault, which is hard to fix.
i agree flash can be a mess. one time, you install kubuntu, install the non-free flash plugin, SUN Java and it all works, a second time, it doesn't. i'm afraid it's very hard to fix it... you might try adding another user to your system, see if it works there. if it does, it's something in your configuration (located in /home/[username]/.kde/share/[config or apps/appname].
good luck...