Is there any medical benefit from giving a 4 yr old breast milk?

No: Humans are just like kittens or puppies, who grow to a certain age and wean off milk... and then eat cat food or dog food. Children grow to a certain age and then eat everything... but do have dairy as a continuing source of calcium and vitamin D. The type of dairy, of course, can be from cows.

Not really: It is a source of fluid/fat/protein/carbs and small amounts of immune factors.However, the relative superiority as a nutrition source fades after about 8 mo when the kid has expanded their intake to include other foods.The immune factors are too diluted by other intake to remain a significant benefit.