With the rise of the Industrial Internet of Things (IIoT), Unmanned Aerial Vehicles (UAVs) have emerged as the preferred sensing tools for data collection. However, resource-constrained UAVs often face challenges in handling complex group key agreement processes, while key management in the flying ad hoc network (FANET) is also susceptible to single points of failure. To address this issue, this paper proposes a blockchain-based continuous group key agreement protocol for FANET. The blockchain is collectively maintained by UAVs and serves to record dynamic changes within the FANET. Additionally, it employs a ratchet tree to integrate a pseudo-random function generator with an updatable public key encryption scheme, effectively mitigating the risk of single points of failure, reducing communication overhead, and enhancing security and self-healing capabilities. Simulation experiments demonstrate that this protocol outperforms existing key agreement schemes in terms of reduced delay and improved security.