Extinction and flame propagation in a meso and microscale channels are investigated analytically. Emphasis was paid to the coupling of wall heat loss, wall preheating, external heat loss and chemical reaction. The results showed that, wall thermal properties, channel width and flow velocity have dramatic effects on the flame propagation and lead to multiple flame regimes and extinction limits. With the decrease of channel width, flame reaches its first quenching limit, the so called critical quenching distance. However, with a further decrease of channel width, the results show that there exists a slow burning flame. With the increase of wall heat loss the speed of the slow burning flame slightly decreases and eventually reaches its second burning limit. With the change of the flow velocity, the results show that sub-limit flame can only exist at flow velocity larger than a critical value. At moderate flow velocity, flame speed increases with the increase of flow speed. At very large flow velocity, flame will be blown off. The above results are confirmed from the recent experimental data.