The spin-flip response of finite nuclei is studied in a fully self-consistent Hartree-Fock plus random phase approximation (RPA) within the SLy5 Skyrme parameter set.The effect of J2 terms and spin-orbit interaction on the response function are discussed.The J2 terms are included/excluded at both the mean field and the excited state for self-consistency.The numerical results show that the J2 terms give a strong effect on the properties of the magnetic dipole response and the Gamow-Teller response.The spin-orbit residual interaction has almost no contribution to the spin-flip response according to our present study.