Self-assembly of ordered structures under the external fields is one of the most important and fundamental research themes in physical science of soft matters including polymers. The "shish-kebab" self-assembly is a most intriguing but fundamental crystalline superstructure formed in polymers under various flow fields. Nevertheless the mechanism of shish-kebab formation is not fully understood yet. In order to clarify the mechanisms for polymer solutions, we have investigated the flow-induced self-assembling structures evolved along a fiber spinning line for concentrated polymer solutions and proposed a new scenario of the kinetic pathway leading to shish-kebab formation and various transient structures evolved therein. The proposed pathway comprises two stages: (i) the early stage pathway before an onset of the birefringence upturn, where the flow-induced phase separation plays a dominant role on creating a series of various transient structures leading to the "sring-like structure" (denoted as "string"), all of which are hardly able to be detected by conventional SAXS, SANS, and WAXD; (ii) the late stage pathway after the onset of the birefringence upturn where the flow-induced crystallization plays a dominant role on generating bundles of stretched chains, probably via the so-called coil stretched chain transition, within the strings grown in the early stage pathway, followed by nucleation-growth of shishs and epitaidal crystallization of kebab lamellae onto shishs from the random coils incorporated within the demixed domains which coexist with shishs within the given string. Our work therefore elucidates an important role of the flow-induced phase separation on the flow-induced shish-kebab formation.