The paper presents the concept of determining the flight trajectory of an unmanned aerial vehicle (UAV) swarm that forms a flying ad-hoc network (FANET) for communication with each other. The FANET allows the swarm to follow a predetermined route between the starting and ending areas performing the reconnaissance task of the most significant area during the flight. The primary limitations of the FANET, which is used by the UAV swarm, are discussed. The radio link range between FANET nodes is based on a power budget and various propagation models. Whereas, for determining the UAV flight trajectories, we propose to use a heuristic algorithm based on the modified Rapidly-exploring Random Tree (RRT). This modification of the base RRT algorithm allows for planning the flight of several UAVs with meeting indicated restrictions, e.g., the minimum distance between individual UAVs ensuring communication between them at any time of the flight. Simulation tests are carried out for a swarm composed of several UAVs in environments with a random number of obstacles, corresponding to a real scenario for search and rescue operations.