Although the fuel pumps are redundant - there are six - during take-off, all fuel is drawn from a single belly tank!!!
Fuel contamination is thus a very likely cause of loss of power in both engines.
Water in the fuel can come from condensation as (during a previous flight) the plane's tanks fill with air as fuel is burned, and this air will likely be very humid if the decent goes through clouds.
The water would sit in sumps in the tanks which should be drained. My guess is that rotation could have caused this water to get out of the sumps, and into the pump lines.
This type of pollution might have been entirely consumed quite quickly, and the engines begun to resume power causing a slight surge in the final seconds, which some observers claim to have noticed - including the sole survivor.
Alternatively, on refuelling, tankers could have been used which had a small amount of a different type of fuel (gasolene or kerosene) - which could have dissolved in jet fuel, and would have burned but producing significantly less power.
The fact that, on crashing, there was a huge fireball, needs to be investigated. If the engines had had a flameout, it is unlikely that jet fuel would have gone up like that - it is essentially Diesel, and you need a blowtorch (or engines still running) to light it. Fire would likely occur, but an instant fireball like we saw is less likely. If there was even a small amount of gasolene present, a fireball is certain.
Either way, the data recording black box will reveal all.
I assume the idea of feeding both engines from the same tank during take-off was the work of Baldrick.