Flow of gas through porous rock can be coupled with solid deformation and gas sorption against the pore walls. This paper starts with the presentation of a thermodynamic constitutive framework for the described three-way coupling in dual-porosity rocks. The developed framework is next applied to the problem of gas flow toward a producing boundary in fractured rocks where sorption concurrently occurs in the rock matrix. The problem involves a set of entangled nonlinearities arising from the coupled processes of sorption and solid strain, resulting changes in rock permeability, as well as the gas equation of state. An analytical solution to this strongly nonlinear problem is developed using the homotopy-perturbation method. The obtained analytical solution is confirmed against a numerical solution to the same problem. The solution rigorously accounts for point-by-point dependence of the involved physical parameters on the pore fluid pressure. Results from a case study indicate that while compaction of the pore space and resulting permeability reduction substantially reduce the gas flow rate, about a third of this rate is due to gas desorption form the pore walls. The effect of the arisen entanglement between gas desorption and rock deformation on gas flow rate is further investigated by identifying the pertinent dimensionless variable groups. In particular, the gas flow rate for a given pressure disturbance at the producing boundary is shown to exhibit nontrivial variations with changes in the values of two dimensionless groups describing the porous frame compressibility of the rock and sorption strength at the pore walls.