In this work, we propose a UAV-assisted multi-layer IC-SDN solution to tackle the content distribution challenges using distributed controllers placed hierarchically in the edge and cloud tiers. Besides, we formulate the traffic optimization problem into a joint forwarding and flow scheduling problem using M/M/1 queueing allocation model and propose a heuristic edge-cloud traffic flow assignment solution that allocates requests based on the service type and device location. We evaluate the proposed solution in a simulation environment considering the mobility principle of FANET nodes. Besides, the effectiveness of the optimization solution and the performance gains are evaluated analytically. The simulation and numerical results show that the proposed optimization model is efficient as compared to other solutions, in maximizing throughput and minimizing computational latency, delay, and packet loss.