I think the easiest way to explain what happen with flaps is as follows:
Selecting flaps creates more drag. Ich think all agree to that. That means a clean aircraft has less drag than with any configuration!
An aircraft with more drag needs more energy.
The energy comes from the engine during climb and cruise and from the component of weight along the gliedpath during powerless descent.
That means that an aircraft with flaps and max power can climb only with a lower ROC or a lower climb angel compared to an aircraft without flaps. During cruise the powersetting is higher, therefore also the fuelflow and the range decreases with flaps and during glide, the glidangel must be steeper with flaps as well as the glidratio becomes worth due to the higher drag with flaps.