Sometimes, children who crave milk to the exclusion of other foods have an inability to completely break down the milk protein, casein. If their gut is leaky, the partially digested casein can leak through into the blood stream where, in the brain, it acts like an opiate (drug-like effect). I am not saying that is what is going on with your kiddo, only that addiction to milk is a major symptom of kids who have this impairment.
My son also makes antibodies to whey (in milk) that cause gastrointestinal distress and inflammation. We avoid dairy and wheat (gluten) because his gut is leaky and he has poor digestion so the partially digested glutein and casien would cause that opiate-like drugging of his brain. Since he has been 3 years old, this is what I did: bought a expensive Vitamix or Blendteq blender (because you will use it every day and the cheap blenders dont get the job done). Use the blender to puree a combination of fruits, vegetables, rice protein powder (or whey protein if you son tolerates), perhaps a kids multivitamin, and a little 100% juice to get it going. I also add some fat in the form of coconut oil or grapeseed oil or other healthy oil in addition to the piece of avacado I often put in. Puree on high speed til smooth. Take a 10cc (ml) syringe that you get at some pharmacies for delivering medicine, obtain a 3 inch length of plastic tubing that you can get at a medical supply store (the kind of tube for IVs or for O2 delivery) or from a pet store (tubing that bubbles air from a fish tank filter) which will fit over the plastic tip of the syringe and give you a nice long nozzle to draw the mixed healthy shake. You can get a section of tube and just cut to desired length. Pipet the shake, 10ml at a time into your sons mouth. Initially and occasionally you may get resistance so sometimes you just have to be insistent. My son is now 7 and we still require him to take his healthy fruit/veggie/protein/oil/vitamin shate every day. He can do it himself (pull up the shake in the syringe) although he has been a bit stubborn lately so we make sure to feed it to him. I also make sure to separately give him some Vitamin D and vitamin K drops in a little oil/juice with added Calcium. The oil helps the VitD absorption and the vitD and vitK together help the Calcium absorption. We do this because he doesn't get any dairy source of calcium. Vitamin A, which is in carrots and other veggies, impairs the Vitamin D/calcium absorption which is why I give the D/calcium separate.
Good luck--you can do it!