Two men who have shared a particular sexual partner consecutively, although not necessarily in quick succession. The essence is, your Milk Brother was the last person to have slept with this particular partner before you did. (Like blood brothers have shared blood, milk brothers have shared milk, at least symbolically.)
Guy at Party: "Why does Javier's girlfriend get all tense, but also kinda flirty whenever Claude is around?"
Guy 2: "She used to bang Claude. In fact, Claude and Javier are Milk Brothers"