Flue gas (CO2/N2) injection into coal seam is promised to achieve both reduction of greenhouse gas emission and enhancement of methane recovery. An improved heat-solid-fluid coupling model governing the equations of coal deformation, fluid transport, heat conservation, and porosity/permeability is proposed. After validating, the mathematic model is applied to simulate the flue gas injection promoted gas extraction with vary schedules of coupling patterns, extraction methods and influencing factors. Results show that the proposed model has coupled the complex interactions among solid deformation, multi-flow of ternary gases and water, gas competitive sorption and thermal transfer. The CH4 pressure varies greatly between proposed model and fluid flow model, demonstrating large deviation when ignoring heat-fluid-solid interactions. The coal permeability first increases dominated by gas pressure drop, and then decreases as the arrival of injected flue gas. Flue gas injection prevents permeability from sharp reduction and deterioration triggered by pure CO2 injection. The effective extraction zone of flue gas injection expands faster than that of primary and CO2 promoted extraction. The influencing factors are initial permeability, injection pressure, N2 adsorption strain ratio, CO2 adsorption strain ratio, injection temperature and thermal expansion coefficient successively.