The problem of ignition and extinction for the flow of a compressible fluid with competitive/chain reactions has been considered in the present paper, A typical system of hydrogen-carbon monoxide fuel mixture forming one end of the opposed jet and air the other end has been considered for the numerical study. An efficient numerical procedure has been developed for the solution of two coupled and non-linear second order differential equations describing the chemical kinetics. The present study reveals that the mass flow rates at extinction (Apparent Flame Strength) for the mixture can be obtained by using a simple mixing rule similar to those used in theories of flame propagation. The results of maximum volumetric heal release rates have been obtained and compared with the experimental results of Bittker and Brokaw.