Cats, like humans, can develop lactose intolerance as they age. Some cats can tolerate milk, and some can't. Giving cats a small amount of milk, then watching for signs of lactose intolerance for 24 hours, determines whether or not they can have milk.
Signs of lactose intolerance are vomiting and diarrhea within eight to 12 hours of ingesting the milk. Cow's milk shouldn't be given to kittens that are not getting enough of their mother's milk. There is more lactose in cow's milk than the kittens can handle. They should be given a cat milk replacer available at pet stores and veterinarians.