Floods are the most common disaster in the world and cause deaths, damages to houses, buildings, and possessions, as well as disruption to communications. In such dynamic scenarios, it is needed to search and track mobile objects transported by the water flows, such as humans, animals, vehicles, and debris. The use of Unmanned Aerial Vehicles (UAVs) is essential in disaster scenarios to help first responders determine correct procedures in terms of searching, tracking, and rescuing the victims, as well as in defining the actions to minimize the risks in a sustainable and timely manner. However, the tracking of mobile objects and the delivery of real-time video sequences from UAVs with energy constraints toward first responders is still a hard task. Therefore, it is necessary to orchestrate a swarm of UAVs for searching and tracking objects while reacting fast to frequent changes in the topology and trajectory, as well as distributing real-time video flows with quality level support to the ground team. This article proposes an energy-aware swarm-based and mobility prediction scheme for UAVs, called SUAV. SUAV provides a unique UAV-based system for rescue scenarios with mobile objects and with support for route and path planning, searching and tracking procedures, mobility prediction and multi-hop communication management, video delivery with Quality of Service (QoS)/Quality of Experience (QoE) support, and energy-efficiency. Simulation results show the efficiency of SUAV in transmitting real-time video flows with QoS/QoE support while minimizing the energy consumption in flooding scenarios with mobile targets.