Microfractures are commonly observed in coal reservoirs. During the coalbed gas production process, stress sensitivity and coalbed gas viscosity changes are significant factors that affect gas transport. By using research methods based on desorption theory and elastic-plastic mechanics, a coal confined microfracture gas transport model that considers dynamic microfracture width variations and gas effective viscosity is established in this paper. This model comprehensively fuses the Knudsen diffusion model, the slip flow model, the surface diffusion model, and the cubic grid model. The reliability of this model is verified via molecular simulations, and the influence factors of gas transport capacity in confined microfractures of coal reservoirs are then discussed in detail. The results demonstrate the following findings. (1) The analyzed flows are well simulated in coal confined microfractures by the model established in this paper, which considers stress sensitivity and coalbed methane viscosity change. (2) Under low formation pressure (less than 5 MPa), the effective gas viscosity rapidly decreases with the decrease in formation pressure, and the negative contribution of gas viscosity change to the microfracture permeability of coal is large. The smaller the initial fracture width of coal, the more obvious this negative effect. (3) When the initial fracture width is fairly small (near 1 nm), Knudsen flow and surface diffusion greatly contribute to the microfracture permeability of coal. However, the larger the initial microfracture width, the smaller the contribution of the two flow regimes to the microfracture permeability, and the permeability is mainly provided by slip flow. (4) Under given conditions, the microfracture permeability of coal is positively related to rock mechanical parameters (Young's modulus and Poisson's ratio) and negatively related to fracture compressibility. Under low formation pressures (less than 15 MPa), the microfracture permeability of coal is positively related to gas desorption. When the formation pressure exceeds 15 MPa, the influence of gas desorption performance on permeability is nearly constant.