Compound droplets have wide applications in various fields such as chemical engineering, medicine, and biological detection. The size and shell thickness are the key characteristic parameters in the application of compound droplets, and studying the dynamic characteristics of compound droplets is of great significance for establishing corresponding manipulation methods, which is helpful to further realize the on-demand production of compound droplets. In this study, Y-shaped and T-shaped bifurcation structures were prepared using microfluidic technology to investigate the flow behaviors of double emulsion droplets (referred to as double emulsion droplets) at the bifurcation structures. Based on the number of the inner and outer droplet breakups, the flow patterns were categorized into three types: twice breakup, once breakup, and non-breakup. The transition law of flow patterns and the influence of droplet length on the transition of flow patterns were analyzed. The evolution processes of characteristic parameters such as the inner and outer droplet extension length, neck width, and gap width were discussed to elucidate the corresponding dynamic characteristic, the droplet movement processes were divided into three stages: squeeze, transition and recovering in the non-breakup mode, and squeeze, transition and fracture in the once breakup and twice breakup modes. It was found that an increase in droplet length effectively reduces the gap width between the droplet and the channel, leading to increased squeezing and shearing forces on the double emulsion droplet, promoting droplet splitting. Based on well-established single emulsion droplet theories, critical splitting conditions for inner and outer droplets were separately formulated, the splitting critical line of T-shaped bifurcation structure was higher than that of the Y-shaped bifurcation structure. Furthermore, the capillary number and initial length of inner and outer droplets were identified to determine the distribution of flow patterns, and a flow pattern map was constructed, effectively delineating different pattern regions. It has important reference value for regulating the characteristic parameters of double emulsion droplets.