Shale gas reservoirs have complex pore structures, consisting not only of nanopores within and between organic grains but also of microcracks distributed randomly within the matrix. Although free gas and adsorption gas coexist, free gas is stored in pore spaces, and adsorption gas is stored in organic matter and clay minerals. Due to the presence of organic matter and heterogeneity in shale, the gas transfer mechanism is complicated involving multiple scales. Gas flow in shale does not conform to the characteristics of linear seepage at the low-velocity stage given the occurrence and flow state of different gases under different pressures. Meanwhile, very few studies have been performed on the low-velocity seepage characteristics of different gases in shale. Therefore, it is important to present experimental evidence for the low-velocity seepage law of different gases in shale. The present study uses experimental simulations of gas mass transfer at multi-scales to investigate the low-velocity gas flow and stress sensitivity of shale core samples. The results indicate that the shale matrix has a strong adsorption capacity, and that its helium flow capacity is 1.5–2.0 times greater than that of methane without backpressure. With increasing pore pressure, the combined action of gas adsorbed to the cavity and free gas leads to first an increase and then a decrease in the flow capacity of methane. With a low confining pressure, the permeability decreases exponentially. On the other hand, as the net confining pressure increases, the core fracture closes, causing the gas slip effect to increase permeability. The results of the study may provide valuable guidance in understanding gas flow in shale matrix and in the development of gas reservoirs.