Funny you should ask! Yesterday I went with my youngest son to the local game shop to return his Xbox 360. Like many game shops, they have a simple policy of "you bring it in, and we give you a refurbished unit under a new 1-year warranty."
Being an engineer, I asked the shop owner just how the Xboxes were "refurbished". When I told him I was a process engineer especially interested in circuit board rework, he wanted me to look at his rework process.
It consisted of a single Airvac DRS 25 rework station. No wash process, no X-ray, no nothing else. But it worked! All he had to do was add flux and reflow two BGAs. 95% of the time that fixed the problem. 4% of the time replacing the two BGAs fixed the problem if the reflow alone did not. Just 1% of the time it was some other component.
Being a commercial product, the Xbox was most likely originally assembled with a no-clean flux and the original flux residues may still be present. Previous reworks would also most likely have been done with no-clean flux.
Because the no-clean flux residues are probably still present under the BGAs, you certainly do not want to use a water-soluble flux, as you may not have a good enough wash process that would subsequently wash both the no-clean flux residues mixed with the organic water-soluble flux residues, and this would lead to short-term reliability issues, especially when you consider the heat and power sources present under those particular BGAs inside the relatively hot Xbox during its operating environment.
Therefore, in this situation I recommend that for reflow-only rework, mask off the BGA (build a tape fence around the BGA) and then a liquid no-clean flux should be applied, and then the excess flux be blown out using a grounded air nozzle set at 20 psi or less.
Do not allow the excess liquid flux to get on the rest of the circuit board. Sufficient no-clean flux will then remain on the solder balls to facilitate good wetting during a simple reflow, without having liquid blobs under the BGA that can cause the solder balls to short during reflow.
For removal and replacement of the BGAs, the best method would be to remove the old BGA, prep the pads by removing the old solder. I prefer the wick method, not the hot air vacuum, as this is much less stressful on the many vias inside the PWB under the BGA. Localized cleaning of just the BGA area can then be performed.
Then apply a very thin layer of no-clean tacky flux that is halide-free. You can then reflow the new component in place.