I would think any pain would indicate there are stones ready to come out, so there's not much need to wait for them to "fall down" between flushes.
On the other hand, I would imagine the dehydration, dialation of the ducts and passage of stones through our organs would necessitate some R&R time.
This is purely conjecture, but it may be safer to do them closer together if the results were poor. I had a weak first flush, and did the second one 12 days later, partly because I didn't do the proper preparations. My second flush was a bumper crop, so I'm going to give my body a full 3 weeks to recover.