Unmanned Aerial Vehicles (UAVs) are used for a wide range of applications. Due to characteristics such as the ability to hover and carry cargo on-board, rotary-wing UAVs have been considered suitable platforms for carrying communications nodes, including Wi-Fi Access Points and cellular Base Stations. This gave rise to the concept of Flying Networks (FNs), now making part of the so-called Non-Terrestrial Networks (NTNs) defined in 3GPP. In scenarios where the deployment of terrestrial networks is not feasible, the use of FNs has emerged as a solution to provide wireless connectivity. However, the management of the communications resources in FNs imposes significant challenges, especially regarding the positioning of the UAVs so that the Quality of Service (QoS) offered to the Ground Users (GUs) and devices is maximized. Moreover, unlike terrestrial networks that are directly connected to the power grid, UAVs typically rely on on-board batteries that need to be recharged. In order to maximize the UAVs' flying time, the energy consumed by the UAVs needs to be minimized. When it comes to multi-UAV placement, most state-of-the-art solutions focus on maximizing the coverage area and assume that the UAVs keep hovering in a fixed position while serving GUs. Also, they do not address the energy-aware multi-UAV placement problem in networking scenarios where the GUs may have different QoS requirements and may not be uniformly distributed across the area of interest. In this work, we propose the Sustainable multi-UAV Performance-aware Placement (SUPPLY) algorithm. SUPPLY defines the energy and performance-aware positioning of multiple UAVs in an FN. To accomplish this, SUPPLY defines trajectories that minimize UAVs' energy consumption, while ensuring the targeted QoS levels. The obtained results show up to 25% energy consumption reduction with minimal impact on throughput and delay.