I think the KS topic has been covered pretty well at the AOPA medical forum. At least my story is there.
The way it was explained to me:
Kidney stone episode = self ground until your urologist is able to tell you honestly that it is not an issue anymore. That usually happens after you capture the stone and he/she is convinced it has left your system.
At renewal time - you will need an x-ray and a report from the urologist that are less than 90 days old that show that you are clean. The AME can issue.
Things change substantially if your x-ray shows any residual stones - you will need to find a more qualified person than me to answer that.
Recommend you search the AOPA medical forum for "Kidney Stone". You'll probably find a half-dozen threads.