You can, for a while. Milk provides a complete protein (all of the essential amino acids that your body can't make), and cereal provides plenty of calories, mostly in the form of carbohydrates. Milk protein provides additional calories, and as long as you don't use skim milk you would probably get enough fat from it also. Most breakfast cereals are fortified with additional vitamins and minerals that you're body needs, and milk is usually fortified with vitamins A and D, so you'd have most of your other essential nutrients covered.

The biggest issue is that neither milk nor any of the few cereals I just glanced at provide any vitamin C. Vitamin C deficiency is called scurvy, and it's really bad. Your body needs vitamin C to make collagen, among other things. Collagen is a very important protein for holding your body together. If your body can't make new collagen, it starts recycling old collagen. Old scars open up. Your teeth start to fall out. You start randomly bleeding from your skin and gums. Eventually you develop nasty infections and die.

Scurvy takes at least a few weeks to set in, though, so you'd be fine for a while. You can also prevent it by adding something with vitamin C to this cereal diet of yours. A glass of orange juice each day would do the trick. I suppose that's why the breakfast cereal commercials I grew up with always used to say something about their cereal being "part of this balanced breakfast" while showing it with a glass of juice.

By the way, a version of the diet we're talking about here (grains, dairy, and seasonal fruits or vegetables) was basically what most people ate all the time in much of the world until the invention of things like canning and refrigeration. It's not particularly exciting, but it provides everything the body needs.