Does extension of flaps 1, 2, 5 or 10 increase descent rates?
It depends what you intend to do with the speed. If all you are looking for is absolute descent rate:  a high-speed, spoilers out and high speed dive will get you the best rate.

What you are usually interested in a normal approach however is not descent rate (vertical speed) as much as descent angle. In this respect, all/any flaps will decrease the L/D ratio, which is going to increase you descent angle. Each stage of flaps will have increasingly higher descent angles, but mind you at a lower speed.