if you do NOT need the file to run from the OS, like a regular system screen saver, you could create a javascript fxn to randomly assign the window's location (size, whatever). have a look at these pages to see each part of your fxn explained:
if, however, you want to execute the file from the operating system like a real screen saver, i did find this freeware bit (googled "Flash screen saver tutorial", hit buried on fifth page)
Martin, what program are you going to use to turn your SWF into a screensaver installer? Check that programs' documentation... Programs like that usually have either switches during the building of your screensaver or AS commands you can insert into your movie that will do this.
the process is usually create a swf
convert swf to projector
use screensaver software that creates an installer which basically is a file that tells the OS to launch your projector whenever the screensaver is supposed to kick in.
it helps to use fscommands in your original swf to set the projector to run fullscreen. the screensaver programs these days are highly advanced and let you customize a lot of settings post swf production.
to answer your question about random placement you need to have a movieclip in your main movie that randomly positions itself by placing AS in its last frame like this: