While there have been important advances within wireless communication technology, the provision of communication support during disaster relief activities remains an open issue. The literature in disaster research reports several major restrictions to conducting first response activities in urban areas, given the limitations of telephone networks and radio systems to provide digital communication in the field. In search-and-rescue operations, the communication requirements are increased, since the first responders need to rely on real-time and reliable communication to perform their activities and coordinate their efforts with other teams. Therefore, these limitations open the door to improvisation during disaster relief efforts. In this paper, we argue that flying ad-hoc networks can provide the communication support needed in these scenarios, and propose a new solution towards that goal. The proposal involves the use of flying witness units, implemented using drones, that act as communication gateways between first responders working at different locations of the affected area. The proposal is named the Flying Real-Time Network, and its feasibility to provide communication in a disaster scenario is shown by presenting both a real-time schedulability analysis of message delivery, as well as simulations of the communication support in a physical scenario inspired by a real incident. The obtained results were highly positive and consistent, therefore this proposal represents a step forward towards the solution of this open issue.