Low-damping magnetic insulators are essential for pure spin current-based electronics as they can generate and transfer spin currents without associated charge currents. Nanometer-thick epitaxial thin films of low-damping magnetic insulators are particularly important in order to control and switch the magnetization via spin transfer torques. We have recently developed films of the ferromagnetic insulator MgAl0.5Fe1.5O4 (MAFO) with a low Gilbert damping parameter (∼0.001). In contrast to Y3Fe5O12 (YIG), MAFO films can be grown on a variety of substrates and have significant in-plane magnetic anisotropy, leading to higher spin-wave frequencies. Here, we demonstrate efficient spin current injection from MAFO into adjacent Pt and β-W layers by ferromagnetic resonance (FMR) broadening and inverse spin Hall effect measurements. Angular dependent magnetoresistance (ADMR) measurements indicate that the proximity effect magnetoresistance is small compared to the spin Hall magnetoresistance associated with spin pumping. FMR and ADMR measurements indicate that MAFO/Pt interfaces have a spin-mixing conductance of ∼2 × 1014 Ω−1 m−2, comparable to that of YIG/Pt. These measurements also show that the spin transport can be described by Dyakonov-Perel spin relaxation combined with an extrinsic spin Hall effect (from skew scattering). These results demonstrate the promise of spinel ferrites for spin current-based spintronics.