Yeah, 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."
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.