Flaps increase lift and drag, and of course the flaps on the 777 and other airliners also increase the wing area. But the later stages of flap are almost all drag-producing, and provide little if any lift. I don't know the 777, but I wouldn't be surprised if the flap setting normally used on a powered approach would be far too draggy if the power fails and there is a sudden need to stretch the glide.
Reducing flap to get rid of the drag, but not reducing it to a point that significant lift starts to be lost as well, will not result in any sink and will be benficial to an aeroplane in the situation that 777 found itself in.
SSD