If -nothing- else is changed when putting flaps down, yes, they "add" lift. The airplane will change its attitude due to the increase in lift... and the increase in drag... and the change in the pitching moment.
All of these sum together.
For a takeoff, the "extra lift" is removed after getting airborne.
Consider a plane of X pounds, dumping flaps that give .25X more "lift". The weight of the plane is still X. -Something- has to change in response to the flap change which would, uncorrected, do something (probably drastic) to the plane.
The controllable variables are: power, and pitch angle.
The drag increase will require power to maintain level flight.
Or, the plane's nose can be lowered to the desired descent rate/path, and power reduced.