You do not have to restart KDE.
Configure Konqueror - Plugins:
List all location of Mozilla and Netscape plugins, mine are /usr/lib/<browser>/plugins
Click the button "scan for plugins"
It will tell you need to save changes first (if you didn't already)
Now go to the Plugins tab:
Check that the flashplayer plugin is listed - it may be listed for each location it was retrieved from.
If all is OK, flash should work in konqueror.
That being said, Flash does not work perfectly in Konqueror. There are websites where it does not work correctly.
I usually test my flash installs at miniclip.com. There are some flash based games there. Moz works well. Kong displays fine, but the keyboard control do not work. Right click on any flash display and you will see "About Macromedia Flashplayer 7..." in the menu if flash is installed correctly - even if it does not work right.