Dynamics of flame kernel evolution with and without external energy addition was investigated analytically and numerically. The effects of radiation heat loss, ignition power, and Lewis number on the correlation and transition between the initial flame kernel, the self-extinguishing flame, the flame ball, the outwardly propagating spherical flame, and the propagating planar flame were studied. The present study extended previous results by bridging the theories of the non-adiabatic stationary flame balls and traveling flames and allowing rigorous consideration of radiation heat losses. The results showed that the effects of radiation heat loss played an important role in flame regimes and flame transition and resulted in a new isolated self-extinguishing flame. Furthermore, it was found that radiation heat losses significantly increased the critical ignition radius and resulted in three different dependences of the minimum ignition power on the Lewis number. Comparisons between the numerical simulations and the analytical results showed a good agreement. The results suggested that prediction of flame initiation without appropriate consideration of radiation is not acceptable.