Video streaming has become a kind of main information carried by Unmanned Aerial Vehicles (UAVs). Unlike single transmission, when a cluster of UAVs execute the real-time video shooting and uploading mission, the insufficiency of wireless channel resources will lead to bandwidth competition among them and the competition will bring bad watching experience to the audience. Therefore, how to allocate uplink bandwidth reasonably in the cluster has become a crucial problem. In this paper, an intelligent and distributed allocation mechanism is designed for improving users’ video viewing satisfication. Each UAV in a cluster can independently adjust and select its video encoding rate so as to achieve flexible uplink allocation. This choice relies neither on the existence of the central node, nor on the large amount of information interaction between UAVs. Firstly, in order to distinguish video service from ordinary data, a utility function for the overall Quality of Experience (QoE) is proposed. Then, a potential game model is built around the problem. By a distributed self-learning algorithm with low complexity, all UAVs can iteratively update their own bandwidth strategy in a short time until equilibria, thus achieving the total quality optimization of all videos. Numeric simulation results indicate, after a few iterations, that the algorithm converges to a set of correlation equilibria. This mechanism not only solves the uplink allocation problem of video streaming in UAV cluster, but also guarantees the wireless resource providers in distinguishing and ensuring network service quality.