The objective of this study was to evaluate the effect of injecting flue gas (CO2, N2, and O2) originating from coal-fired power plants into a coal seam on CH4 extraction and CO2 geological storage. To this end, a multifield thermal–fluid–solid-coupled mathematical model of flue gas injection extraction was established. The results showed that with the time increase, the volume concentration of CH4 decreased, but the CO2, N2, and O2 increased. Compare with single extraction the gas injection extraction brought about a significant reduction in the pressure and content of the CH4, an increase in the CH4 extraction rate, and an increase in the effective radius of CH4 extraction. In the single extraction, the temperature of the reservoir decreased, and its permeability increased. In the gas injection extraction, the temperature near the gas injection hole increased, whereas the temperature near the extraction hole decreased, and the permeability decreased overall. A method of measuring the effective radius of gas extraction by temperature is presented. The storage and extraction time of CO2 exhibited a linear relationship, and the CO2 escape rate increased gradually. The longer gas injection extraction the time, the greater the risk of coal and gas (CO2) outbursts.