, you should be able to add the packages without causing any problems to your system (as long as you have space in your Linux partition). I never use KDE but I have it installed so I can use the applications in XFCE (I only use a few, but the few I use are important for me). Furthermore, you don't have to have everything KDE installed. So, unless I'm mistaken, you already have QT. The other things you'll need will be kdebase, kdelibs, arts, and kdegames. You can get these all from http://packages.slackware.it
. On that site you'll see a box with the title Search for packages or file names
. Change the first field from slackware-current to Slackware 12. Then do your searches for kdebase, kdelibs, arts, and kdegames. Download each file to somewhere in your home directory. Open a terminal emulator (Terminal, xterm, whatever), and type "su" at the prompt, then when prompted type your root password. Change to the directory where you downloaded the packages. Then type "installpkg" followed by the full file names of kdebase, kdelibs, arts, and kdegames. They should then install. I don't think the games will appear in your Fluxbox menu, but you can just start kbackagammon by typing "kbackgammon" in a terminal.
One caveat: I'm no expert at these things but in the past I've installed just the base KDE packages in order to get one app, and it works. Nevertheless, I can't guarantee anything so proceed at your own risk.
I know this seems like a lot for just one game, but if you like backgammon, ... it might just be worth it.
Addendum: No, adding kdebase, arts, libs and games should not affect the xfce base. At this level this stuff is pretty modular and fairly well segregated from other things.