Green ammonia has become an increasingly popular fuel in recent years because of its combustion process without carbon oxide release. Adding ammonia to methane fuel for co-combustion has become one of the important research topics in the current combustion field. In the present study, the CH4/NH3/Air counterflow diffusion flame was taken as the research object, and Chemkin-2019 R3 software was used to explore and analyze the flame extinction limit and chemical kinetics characteristics under different ammonia mixing ratios, initial pressures, and air preheating temperatures. It was obtained that the flame extinction stretch rate was decreased by increasing the NH3 mole fraction in the CH4/NH3 mixed fuel. The increase in pressure or air preheating temperature would accelerate the chemical reaction rate of each component in the combustion process, increase the flame extinction limit, and counteract the "stretching effect" of the flame, thus restraining the flame extinguishing phenomenon. The results of a path analysis show that the formation and consumption of OH had an important influence on flame extinction in the chain reaction. The net reaction rate of OH increases with increasing the initial pressure or air preheating temperature, which leads to an increase in flame intensity, combustion stability, and the extinction limit. Furthermore, the function curve between the reaction influences the RIF factor and the stretch rate of the first-to-ten reactions, affected by the heat release of flame combustion, was drawn and quantitatively analyzed. Eventually, a sensitivity analysis of the flame under different working conditions was completed, which found that promoting the forward reaction R39 H + O2<=>O + OH also promotes the positive combustion as a whole when the flame was near extinction. The sensitivity coefficient of R39 in the CH4/NH3/Air flame increases with the growing initial pressure. The increasing air preheating temperature was capable of switching the reaction of R248 NH2 + OH<=>NH + H2O in the CH4/NH3/Air flame from an inhibiting reaction to a promoting reaction, while decreasing the sensitivity coefficient of inhibiting the forward reaction R10 O + CH3<=>H + CH2O, R88 OH + HO2<=>O2 + H2O, and R271 H + NO + M<=>HNO + M. Thus, the inhibition effect of flame extinction was weakened, and the positive progress of combustion was promoted.