We theoretically investigate the effect of transverse magnetic anisotropy on spin-flip assisted tunneling through atomic-spin chains. Using a phenomenological approach and first-order perturbation theory, we analytically calculate the inelastic tunneling current, differential conductance, and atomic-spin transition rates. We predict the appearance of additional steps in the differential conductance and a pronounced increase in the spin-flip transition rate which at low voltages scales quadratically with the ratio of the transverse anisotropy energy and the sum of the longitudinal anisotropy energy and the exchange energy. Our results provide intuitive qualitative insight into the role played by transverse anisotropy in inelastic tunneling spectroscopy of atomic chains and can be observed under realistic experimental conditions.