the term is a reference to the American revolution and the Red coat loyalists, who remained on the side of the British during the period leading up to the United States independence.
Harvey: Unlikely, she has a boyfriend.
Greg: That didn't stop me last weekend with Laura.
Harvey: True, but Jenna's a red coat.
2. A British friend you want verbally poke.
American friend: "I made these for you! What? You don't like my biscuits? Ok, this means war, bring it redcoat."