Is gluten in milk
Milk is naturally gluten-free.
Gluten is only in certain grains, most commonly wheat, rye, barley, spelt, farro. If you want to use oats, look for the oats that are labeled gluten free.
The protein in milk is cassein.
Cow's milk is gluten-free. Milk substitutes such as almond milk, soy milk, etc. will sometimes contain gluten. It's always a good idea to read the ingredients on a product, just in case. But you shouldn't have to worry about straight cow's milk.