Unmanned aerial vehicles (UAVs) are crucial tools for post-disaster search and rescue, facing challenges such as high information density, rapid changes in viewpoint, and dynamic structures, especially in long-horizon navigation. However, current UAV vision-and-language navigation(VLN) methods struggle to model long-horizon spatiotemporal context in complex environments, resulting in inaccurate semantic alignment and unstable path planning. To this end, we propose LongFly, a spatiotemporal context modeling framework for long-horizon UAV VLN. LongFly proposes a history-aware spatiotemporal modeling strategy that transforms fragmented and redundant historical data into structured, compact, and expressive representations. First, we propose the slot-based historical image compression module, which dynamically distills multi-view historical observations into fixed-length contextual representations. Then, the spatiotemporal trajectory encoding module is introduced to capture the temporal dynamics and spatial structure of UAV trajectories. Finally, to integrate existing spatiotemporal context with current observations, we design the prompt-guided multimodal integration module to support time-based reasoning and robust waypoint prediction. Experimental results demonstrate that LongFly outperforms state-of-the-art UAV VLN baselines by 7.89\% in success rate and 6.33\% in success weighted by path length, consistently across both seen and unseen environments.