Important role of chemical interaction in flame extinction was numerically investigated in downstream interaction among lean(rich) and lean(rich) premixed as well as partially premixed $H_2$-air and CO-air flames. The strain rate varied from 30 to $5917s^{-1}$ until interacting flame could not be sustained anymore. Flame stability diagrams mapping lower and upper limit fuel concentrations for flame extinction as a function of strain rate are presented. Highly stretched interacting flames were survived only within two islands in the flame stability map where partially premixed mixture consisted of rich $H_2$-air flame, extremely lean CO-air flame, and a diffusion flame. Further increase in strain rate finally converges to two points. Appreciable amount of hydrogen in the side of lean $H_2$-air flame also oxidized the CO penetrated from CO-air flame, and this reduced flame speed of the $H_2$-air flame, leading to flame extinction. At extremely high strain rates, interacting flames were survived only by a partially premixed flame such that it consisted of a very rich $H_2$-air flame, an extremely lean CO-air flame, and a diffusion flame. In such a situation, both the weaker $H_2$-air and CO-air flames were parasite on the stronger diffusion flame such that it could lead to flame extinction in the situation of weakening the stronger diffusion flame. Particular concerns are focused on important role of chemical interaction in flame extinction was also discussed in detail.