BSOD is a hardware fault, or possibly (but very unlikely) a faulty driver.
If you get a BSOD, you have a physical problem with the computer’s physical hardware-- reinstalling software won’t fix it. (Well, maaaybe drivers.)
My new guess is that Facebook, or Flash-in-Facebook is exercising your video card in a specific manner which causes a BSOD. Probably from overheating. You could try just opening up the case and blowing all the grime out, that might be all it is.