Flying ad hoc networks (FANETs), an innovative airborne networking paradigm, are expected to play a vital role in emerging military and civilian applications. However, the dynamic nature of flying nodes imposes significant challenges on efficient routing design. In this paper, considering the frequent changes of topology, we first define a stability indicator and an efficiency indicator for a link and use them as a prior knowledge to enhance the robustness and agility of route discovery. Then, we design a distributed hybrid proactive-reactive ant colony routing protocol tailored for highly dynamic FANETs. Our protocol unifies the data transmission and routing control processes. It gleans the benefits of both a multi-round reactive ant-sending mechanism and a proactive pheromone updating process. Hence, it is well adapted to highly dynamic scenarios while minimizing the routing overhead. Extensive simulation results with ns-3 show that our scheme comprehensively outperforms existing routing schemes in FANETs in terms of latency, packet loss rate, overhead and jitter, especially in highly dynamic scenarios.