If you are worried about vitamin loss, you can give him a children's vitamin. It is not really necessary for a child to drink milk, it's just necessary for him to have a balanced diet and enough fluids to prevent dehydration. If all he will drink is water, simply be sure that some of the other food in his diet gives him calcium, and take care that he gets balanced meals (protein, carbos, fruits, veggies).
There is really nothing much to be worried about your baby unless he is totally malnourished and immunocompromised.You have to understand every baby needs certain amount of nutrients no matter which food provides it.Milk can be replaced by any source of food but not only milk.Ill give you details about that.
• Energy requirement includes basal metabolism, the thermic effect of food, energy required for growth, physical activities, elimination
• Total energy requirement: infant 110 k cal/kg.d, With subsequent decrease of about 10kcal/kg for each succeeding 3yr period
• The distribution of calories protein 10-15%, Carbohydrate 50-60%, fat 35-50%
• The resource of energy: Protein or carbohydrate provides 4 k cal/g, fat provides 9kcal/g
• Water requirement: Infant 150ml/kg.d, rule continue 3yr decrease 25ml
Choose any food that meets these prerequisites.
2.Requirement of cow s milk till term-3 years-
Calculation 5month weight 7kg
Total daily energy need: 7x110=770
The amount of daily milk required: 770ml
The amount of daily water required: 7x150=1050ml
Supply water besides milk: 1050ml–770ml=280ml
Divided into 5~6 times per day
3. Malnutrition is caused only when above mentioned prerequisites not provide adequate nutrients which leads to Marasmus or Kwashiorkor which are main conditions that cause serious consequences due to malnutrition.If you need more details get more questions.
Maybe you are trying too hard, have you tried the flavored milk, choc/ strawberry /banana and it wont hurt him to leave milk alone for a while, at 3 year old I am assuming he eats fruits and veg and protein , children like pasta , rice, beans,give him plenty of fresh water and some juice.Sometimes we worry more than we have to about children eating, if we make more of it more it becomes . So back off let him eat his food and in a very short time he will drink milk again .