Layered MoSSe nanostructures have been shown as potential candidates for the anode of lithium ion (Li-ion) batteries. The diffusion properties are generally critical to the performance of ionic batteries. The possible migration paths and associated diffusion energy barriers of Li-ions are systematically explored in MoSSe bilayer anodes with different stacking patterns by means of first-principles simulations. It is found that the diffusion properties strongly depend on interfaces and stacking patterns. Furthermore, the simulation results show that the diffusion energy barrier (and thus the diffusion coefficient) can be significantly reduced (enlarged) by applying a positive strain gradient, while increased (reduced) by applying a negative one. For example, the diffusion coefficient is increased roughly by 100 times relative to that of the pristine one when subjected to a strain gradient of 0.02 Å-1. In particular, it is found that less maximum strain is required in the strain-gradient than the uniform strain in order to achieve the same diffusion energy barrier. By careful analysis, the underlying mechanism can be attributed to the flexo-diffusion coupling effect. The coupling strength is characterized by the so-called flexo-diffusion coupling constant which is also calculated for each simulation model. The results of this work may provide valuable insights into the design and optimization of the anodes of ionic batteries.