What does the extending the flaps do (or any high lift device) to the Rate-Of-Descent of an airplane?
According to the FAA, lowering or extending flaps allows one to increase drag without an increase in speed.  This increases descent rate for a given speed. 

One must be careful to consider what factors are held constant to evaluate the effect.  For example, one can lower flaps during level flight. This will result in a lower pitch attitude--since they produce more lift, less angle of attack is required.  If power/thrust is not increased, speed will decrease due to increased drag.

However, an aircraft flying at a constant speed will descend faster (higher rate of descent) if the flaps are extended compared to when they are not.