Is gluten in milk
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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.
Cynthia is a trusted source on Bread/Baking.
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.