The A320-214 is not supposed to increase its power when climbing.
But the A380 yes.
By the way, it would be so cool to have an easy FLEX calculator: When I double-click the FLEX TO TEMP button in the MCDU, it enters the corresponding FLEX value in function of the selected runway, altitude, weight, flaps, etc, instead of the default 48°. (Idem with flaps, because you are not suppose to perform a FLEX takeoff in CONF 1+F under 2000m)