Milk is not on Stage I of the King Diet except for the possibility of lactose free milk. I have to admit that I don't know if lactose free milk is available as fat free or with regular fat content. 

But the question remains as to whether fat free milk is healthier than regular 2% fat milk lactose free or not.

Whole (Full Fat) Milk vs Non Fat Milk–Which is Better? is an article from Nutrition WatchDog that you will want to read. 

First of all, any milk you drink should be organic and free of pesticides or cows being fed with feedstock chemically farmed with Monsanto's Round up herbicide (glyphosate).

Secondly, the King Diet saves you from "hemp milk, soy milk, coconut milk, flax milk, almond milk, cashew milk, macadamia milk, oat milk, pea milk, rice milk and even sunflower milk," because they either are not on the diet or have other ingredients that are not on the diet such as sugars, processed vegetable oils, and flavorings. So, even while they sound healthy, they are not. 

For years and years fat got a bad rap and within the last ten of so years the song of fat free being healthier regular milk with fat has been found to be a myth.

Of course, if you live near an organic dairy farm and can get the real thing right from the cow and do your own pasteurization - go for it.
 

In the meantime, if you desire milk go for the fat option and read the well written and explained article,Whole (Full Fat) Milk vs Non Fat Milk–Which is Better? "The French eat plenty of full fat dairy, real butter and cheese, and seem to actually have less incidence of obesity and chronic disease, along with the Swiss, who eat tons of full fat cheese and dairy products. Natives living in the mountains of Eastern Europe routinely live to the ripe old age of 100, consuming full fat dairy and kefir most of their lives. Add to that, the Maasi and Samburu tribes in Africa who eat a very high fat diet, yet are tall, slender and very healthy, with little incidence of any type of diseases."