“Flame-street” is an interesting diffusion flame behavior in which a series of flame-segments is separately distributed along the mixing layer in a narrow channel. This experimental phenomenon was experimentally and numerically investigated with the focus on the steady-state, thermo-chemical flame structures in previous literature. In the present paper, the dynamic formation process of a methane-oxygen diffusion flame-street structure was simulated with a reacting flow solver developed based on the open-source framework OpenFOAM. By imposing a certain amount of ignition-energy near the channel outlet, a reaction-kernel was formed and bifurcated. Subsequently, three separate flames were consecutively generated from this kernel and propagated within the channel. The whole process was completed within 15 ms and all the discrete flames were eventually in a steady-state. Interestingly, different propagation features were observed for the three flame segments: The leading flame experienced a flame shape/type change from a tribrachial structure in its fast-propagating phase to a long, trailing diffusion tail after being anchored to the inlet. The successive flame had a much lower propagation speed, keeping its two wing-like (fuel-lean premixed and fuel-rich premixed) structure while moving toward its stabilization location, which was approximately in the middle of the channel. The last flame, after the ignition source was turned-off, was immediately convected a bit downstream, and eventually featured a similar two-branch-like structure as the second one. Moreover, chemical insights for the premixed and diffusion branches of the leading flame were also provided with the change of significance of some key elementary reactions focused on, in order to attain a detailed profiling of the flame-type transition. This paper is a first-ever one discussing the transient formation of flame-streets in literature and is believed to be useful for obtaining a comprehensive understanding of this unique flame characteristics from a dynamic point of view.