Flux isn't used because it's not suitable for they job; it's not capable of removing the silica layer which forms on the silicon die so the solder would not wet to it. There are various methods of overcoming the problem, one of which is to coat the die with something solder-able, another is to 'scrub' the die and keep it under a protective atmosphere until soldering IIRC. The metal lid is presumably also cleaned and preserved in the same way.
Obviously this is significantly more complex than just squeezing a bit of TIM on the die and plonking the lid on, which is presumably a large part of the reason why it's not used where MFRs can get away with it. And therefore, not really worth attempting at home, although some decent TIM would probably work OK.
Oh and the following is in no way a pop at you (the use of the phrase was clearly relevant), you just reminded me of something. IMO it was fairly amusing to see how many places were parroting the phrase 'fluxless solder' in the IVB fallout, as though it was somehow significant or relevant to the story. I suspect some news source used the phrase and it was subsequently regurgitated around the web without much thought as to what it actually meant. Why not just 'solder'?