I would feed him lots of apples, apple juice and lemonades.

Add a malic acid capsule to one of his meals daily. These things will work to shrink his stones and support his liver and gall bladder to function. It may take time. As long as he is not in pain, keep changing his diet to whole foods and lots of fresh clean water. The stone may never pass, but that does not mean he cannot live well and long with it in there. Wait until he is older for another flush, would be my advice. And if he does have gall stone pain, a teaspoon of Epsom Salts in water should take care of it. Some Epsom Salts baths will help, too. You might consider Iodine supplementation for him as well, as it seems to be inhibiting stone growth in adults.