Magnesium-based materials are promising candidates for solid-state hydrogen storage due to their high gravimetric capacity; however, their practical application is limited by slow sorption kinetics and high thermal stability. This study investigates the influence of hydride additives on the microstructure and hydrogen desorption performance of ball-milled Mg–Co composites. Flake-like magnesium particles modified with 7 wt.% cobalt were processed by high-energy ball milling and subsequently doped with sodium hydride, potassium hydride, and calcium hydride at concentrations of 0.5 and 5 wt.%. Microstructural, phase, and surface chemical characterization revealed that additive type strongly affects dispersion, interfacial distribution, and the formation of additive-derived surface species within the Mg–Co matrix. Hydrogen sorption measurements conducted at 300–350 °C under different pressure conditions show that alkali hydrides significantly enhance low-temperature hydrogen desorption. In particular, the composite containing 5 wt.% potassium hydride exhibits a marked improvement, releasing approximately 4 wt.% hydrogen at 300 °C, while the unmodified material shows negligible desorption under the same conditions. Thermal analysis confirms that the additives modify the dehydrogenation response, although improved performance is not solely correlated with lower onset temperatures. The results demonstrate a clear asymmetry between hydrogen absorption and desorption, indicating that the primary effect of hydride additives is an enhancement in dehydrogenation kinetics. This behavior is associated with microstructural features, including additive dispersion and interfacial effects induced during processing. These findings provide insight into the design of magnesium-based hydrogen storage materials through microstructure–property relationships.