Ikarus:
Here's a short scribe regarding FAA and renal stones. You'd have to consult your own certifying authority also:
Kidney Stones - AOPA
I don't think FAA, at least, likes you flying with retained stones. I expect other agencies are similar. So you have to prove they are gone.
As Gingernut pointed out, there are some things to do to ameliorate stones, but in depends on the type of stone.