While the "report" mentions the possibility, the B777 autothrust does not reduce to prevent "overspeed" of the flaps - in fact no transport's autothrust I have flown does this. There is a load relief function which will accomplish this however. Autothrust is targeted for the FMS or selected speed. On the Airbus, (and I agree, it is a waste of bandwidth to turn this into an A vs B commentary), but the autothrust also targets "over and underspeed" flight circumstances.
The 744, in normal takeoff/climb modes, will prevent flap overspeed. Normally TO/GA is the selected pitch and autothrottle mode, and V2 is set in the MCP. When the autopilot/FD transitions from TO/GA to VNAV, the MCP speed window closes, and speed is controlled by pitch (either by the autopilot if engaged, or manually following guidance from the Flight Director). The current flap limit speed is set by the FMS as the limit speed, so flap overspeed protection IS provided.
HOWEVER, I have no experience in using the autopilot with such a low level-off altitude. I do not know for sure how well the 744 would handle it, so I tend to fly those manually at least until the airplane is stable at the level-off altitude. There are those in the 744 community who would recommend going directly to FLCH after 400' AGL in similar situations -- especially if VNAV ALT was not captured) to reduce the rate of climb and ensure the Autopilot/FD and autothrottles exit TO/GA. I would not disagree with that technique.
Frankly, in that situation the flap limit speed would be among the LEAST of my worries. Keeping above V2 and VERY close to the target altitude would be my primary concerns. ACARS WOULD immediately report the flap overspeed.
A couple hundred people were VERY lucky that there was a 3rd pair of eyes AND a 3rd brain at work on this flight.
In the US we at least have the NASA ASRS reporting program to use without fear of retribution. Many airlines have the ASAP program as well, but it's not confidential like ASRS is. It's too bad the situation is so bad over there in India...