If you have a pump, you could give him breastmilk in a cup for 2-3 days, then start adding just a tiny bit of cow's milk into it. Since you know he doesn't like it already, I'd start with a tablespoon. Gradually increase the milk, one tablespoon more every two days. It will take a while, and it sounds like a royal pain, but if it'll get him to drink milk...
My first son chugs milk and always has. But my second doesn't like to drink it. We get it down him as often as we can, and here are our tricks. First, he always has some with cereal in the morning. When my boys were your son's age, I started them with mini shredded wheat (yes, they were frosted) because they're easy to pick up with a spoon or fingers. I would pour a little milk on top until they were saturated, but not much milk in the bottom (to contain the mess). They loved them, and later I added a little more milk.
My husband always craves milk after dessert (it really does hit the spot!) so we always pour DS#2 some milk, too. He usually drinks it, and he is gradually drinking more.
He also loves yogurt and cheese, which are great ways of getting "milk" down him. He loves quesadillas for lunch (just cheese melted in a folded-over flour tortilla, or with refried beans for fiber and protein spread inside, too) and grilled cheese sandwiches. My husband loves milk and always says I need to drink more, but I am sure we all get enough through other dairy products.