Hiking could make things worse if you get dehydrated, otherwise, hiking is good since exercise helps pass the stones. Passing a kidney stone is very painful for several hours while it moves into the bladder, so you might have to pitch a tent wherever you happen to be if you start to pass a stone. Imagine how you think the trip will be if you end up with severe pain and nausea for a day. The pain will be the same whether you are sitting in a tent or in your bed at home, so as long as you and the people leading the hike know what to expect, it should be OK, but you have to plan as if you know you will pass a stone on the trip.
You should be prepared to put up with very severe pain and nausea when passing a stone - many people go the the emergency room because the pain makes it seem like something is seriously wrong and they can't stand the pain. You should see your doc to get pain medication just in case, and also to make sure the doc thinks its OK.
