There are several forms of kidney stones. Most stones are formed from either uric acid or calcium oxalate.
Nettle leaf is good for dissolving both types of stones. Nettle leaf is excellent for removing uric acid from the body, and it supports the kidneys.
Small doses of juniper berries also stimulate the excretion of uric acid.
Phyllanthus niuri (chanca piedra, "stone breaker") is used to dissolve both kidney and gallstones.
Celery seed, cherry juice and cherry stem tea also remove uric acid.
Vitamin B6 is also helpful for dissolving kidney stones.
Of course drink plenty of water and cut out most protein from the diet. Avoid all alcohol. Alcohol inhibits the excretion of uric acid, and beer in particular is high in purines that convert to uric acid increasing the uric acid load.
For oxalate stones I recommend nettle, and increasing your magnesium, not calcium, intake. Also avoid cooked kale and spinach, as well as chocolate, and other high oxalate foods.
Vitamin C (ascorbic acid) is broken down in the intestines in to oxalates. In some individuals these oxalates can be absorbed increasing the risk of oxalate stones.
On the other hand ascorbic acid does help to dissolve phosphate stones.
You should also be checked for possible contributing factors, such as hemolytic anemia.