Gas transport in coal and shale matrices does not always fall into the continuum flow regime described by Darcy's law. Rather, a considerable portion of this transport is sporadic and irregular when the mean free path of gas becomes comparable to the prevailing pore scale. A nonlinear process influenced by non-Darcy flow components like gas sorption, gas slippage, and diffusion occurs throughout gas recovery. Therefore, a new permeability model with pressure-dependent weighting factors is presented to describe gas flow. This model contains the coupling of matrix flow with explaining the impact of both multiple flow regimes and stress-strain relationship on unconventional gas permeability evolution. The stress-strain relationships were derived from thermal-elastic equations and can be incorporated into the fracture-based flow component, enabling permeability prediction under uniaxial strain and hydrostatic conditions. The "U-shape" permeability trends caused by flow dynamics and geomechanical effects are observed in modeling results, which match experimental data. The agreement between modeling results and experimental data shows that gas permeability can be fully characterized by the presented model. This model has the ability to predict uniaxial strain permeability to hydrostatic permeability in a laboratory scale.