As someone who suffers from the dammed things (enough so that Social Security eventually admitted I was disabled due to them) my guess is they don't work much differently in space than they do on Earth. The primary reason they move inside the ureter, causing massive amounts of pain, is due to urine flow. I believe that works the same way in space, or at least I've never heard of it acting significantly different.
As to forming stones in the first place, I don't know if being in space has any impact on that or not. Given how horrifically painful stones are, I'm pretty sure we'd have heard about it long ago if being in space significantly increased the risk of stone formation. Astronauts are tough, but stone pain can cripple the toughest of the tough with ease.
