If I understand it right (I'm not a medical professional) kidney stones can be caused by different things. So if you want to donate a kidney the doctors will want to see waht the cause of YOUR bout was, in order to get a good idea about whether you would be prone to them in the future. If you just have one kidney left, a stone would be a big problem. Likewise, they have to be sure that the kidney you are donating is in good condition. So it is, I think, worth looking into. Your previous bout with kidney stones MIGHT exclude you, but perhaps might not, depending on the causes. It would be worth making the offer and then letting the doctors decide.
best wishes,
Fr. Pat