A lightened flywheel does not increase the engines power but the reduced mass will mean it spins up faster. Depending on how much weight is removed from the fly, its like removing 300kg of the cars weight in 1st gear, this ratio declines as you go up the gears. It will be hardly noticable at all in 4th 5th and 6th. Basically the car will accelerate much much quicker in 1st 2nd.
There is a complicated calculation to work it all out.