Unmanned aerial vehicle (UAV) has been widely adopted in wireless systems due to its flexibility, mobility, and agility. Nevertheless, a limited onboard battery greatly hinders UAV to prolong the serving time from communication tasks that need a high power consumption in active RF communications. Fortunately, caching and backscatter communication (BackCom) are appealing technology for energy efficient communication systems. This motivates us to investigate a wireless communication network with backscatter- and cache-assisted UAV technology. We assume a UAV with a cache memory is deployed as a flying backscatter device (BD), term the UAV-enabled BD (UB), to relay the source's signals to the destination. Besides, the UAV can harvest energy from the source's RF signals and then utilizes it for backscattering information to the destination. In this context, we aim to maximize the total throughput by jointly optimizing the dynamic time splitting (DTS) ratio, backscatter coefficient, and the UB's trajectory with caching capability at the UB corresponding to linear energy harvesting (LEH) and non-linear energy harvesting (NLEH) models. These formulations are troublesome to directly solve since they are mixed-integer non-convex problems. To find solutions, we decompose the original problem into three subproblems, whereas we first optimize the DTS ratio for a given backscatter coefficient and UB's trajectory, followed by the backscatter coefficient optimization for a given DTS ratio and UB's trajectory, and the UB's trajectory is finally optimized for a given DTS ratio and backscatter coefficient. Finally, the intensive numerical results demonstrate that our proposed schemes achieve significant throughput gain in comparison to the benchmark schemes.