I say, and with God's success: It is not permissible; because it is a condition for the permissibility of removing impurity with a liquid other than water that the liquid must be pure, liquid, and capable of removing the impurity, which is not realized in milk. See: Al-Bahr Al-Ra'iq 1: 234, Al-Binayah 1: 710, Radd Al-Muhtar 1: 205, Naf' Al-Mufti p. 135, and God knows best.