Yes he does eat fruit. Apples, Pears, white grapes. anything with a white or colorless middle. He also eats meat as long as it is not fried. It also can have any grill marks. I have become a whiz at that.
I think you should at least cut out the milk for starters if he is not having regular bowel movements. There are other alternatives available, such as almond milk, potato milk ( Vance's Dari-free - very good), Rice Milk, etc. He may not want to drink it plain, but he can certainly use it on his cereals or in other food preparation.
Does he eat fruit? If so, pears might be a good choice as they don't have any color.
I have a very picky eater. My son is 11 years old and only eats food with no color. Oh and no foods can be mixed or touching..breads and dairy products are his fav... The bread was easy to subsitute at the health food store with GF free products.