Let's say you need greater descent rates than you can get with the full use of the speed brake in an airliner. Does it help to use the above flap positions in getting greater 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.
As @Radu094 said, a spoilers out, high speed dive will generally get you the highest rate of descent. For that max rate of descent you would put your airspeed right up against the limit.
Using the 747-100/200 as an example, that max airspeed is 350 knots as I remember, and you don't have the option of also using flaps because operation of the speed brakes with any degree of flaps is prohibited.
Even if the speed brakes prohibition wasn't there, the max speed on a -200 for flaps 1, 5, 10 is 275, 250, 238 respectively, considerably lower than the 350 knots for the max rate of descent with a clean wing.
You could extend the gear. Speed brake usage with the gear extended is allowed, and the max gear-extended speed is 320 kn. Though 30 kn slower than than the max speed without the gear, all that drag allows you to put the nose down further. I can't remember how the rate of descent in this configuration compares with gear-up 350 kn, but you'll have a much steeper angle (and a lot more noise), and you really come out of the sky.
There's a trade-off though. While the max gear-extended speed is 320 kn, the max gear-operation speed is 270, so you have to first slow down before using the 320 kn speed.