The presence of hydrogen (H) can detrimentally affect the mechanical properties of many metals and alloys. To mitigate these detrimental effects requires fundamental understanding of the thermodynamics and kinetics governing H pickup and hydride formation. In this work, we focus on H diffusion in Zr-based alloys by studying the effects of alloying elements, vacancy and stress, factors that have been shown to strongly affect H pickup and hydride formation in nuclear fuel claddings. Parameterized by DFT calculations, a recently developed accelerated kinetic Monte Carlo method is used for the study. It is found that for the alloys considered here, H diffusivity depends weakly on composition, with negligible effect at high temperatures. In contrast, H diffusivity is affected by stress strongly. In addition, H diffusivity is impeded under relative high vacancy concentration.