With the large number of cameras deployed in smart industrial parks and smart campuses, edge devices and location-fixed edge servers are deployed near to these cameras and help transmit video streams to data center for video analytics; however, location-fixed edge servers are difficult to adapt to computation-intensive and delay-sensitive video analytics tasks in hot spot, and it is also challenging to execute tasks in natural disasters in which the infrastructure is damaged. Moreover, task migration methods are used to balance the load of edge servers caused by irregular movement of detected objects, but it results in extra data transmission overhead. Therefore, unmanned aerial vehicles (UAVs) with computing and communication resources are widely used to optimize mobile edge video analysis; however, existing solutions formulate the UAV-based lowest latency and energy consumption by jointly optimizing the task allocation strategy and UAV location to be a multiobjective optimization problem, based on which the Pareto optimum solution set, including task allocation strategies and UAV locations, can find multiple solutions but not a unique solution. It makes the solution difficult to be applied in video analytics with the UAV hover location decision-making scheme and task allocation strategy. In this article, we propose a flexible cloud-edge collaborative scheduling strategy based on a UAV namedFlexEdge. We first normalize values of execution time and energy consumption, and then convert the multiobjective optimization problem into a single-objective optimization problem by using the weighted sum of the two metrics as the optimization objective. We also proved the task allocation strategy based on execution time, energy consumption, and the UAV hover location decision-making scheme as an NP-hard problem. We propose a flexible and lightweight genetic algorithm (FGA) based on a polysomy-strengthening elitist genetic algorithm in FlexEdge to address the NP-hard problem. FlexEdge not only achieves optimal task allocation and UAV location to minimize the weighted sum of execution time and energy consumption but also provides computing resources and reliable network connection to reduce task offloading overload, which is validated by comprehensive performance evaluation.