Does milk have antioxidants? Hardly. To put into perspective how low it is, consider the fact that even Budweiser beer has 3x the amount when comparing equal weights. The measurement of how much antioxidants there are in 1% reduced fat milk is the same number as fried chicken. Raw and organic sources of dairy do not make much of a difference, either.
Research Support, Non-U.S. Gov't: Carlsen MH, Halvorsen BL, Holte K, et al. Nutrition Journal NIH 2010