Autonomous UAV swarms have great potential for applications such as search‐and‐rescue, wildfire monitoring, and environmental mapping, but rapid and reliable coverage of large, obstacle‐filled areas remains challenging. In this paper, we ask: How can decentralised multi-UAV systems be optimised for large-scale priority-aware exploration? To answer this, we present the Fast LIDAR-based Autonomous Multi-UAV Explorer (FLAME), a hierarchical framework for efficient swarm exploration with long‐range, 360° LIDAR sensors. Locally, a dual‐mode exploration planner alternates between high‐speed straight‐line travel and frontier-cost‐based exploration. Globally, each UAV’s mission is optimised to visit user‐defined high‐priority regions early while minimising total mission time, enabling decentralised coordination with minimal duplicate exploration. FLAME also integrates battery‐constrained multi‐mission planning, dividing large tasks into multiple battery‐feasible missions with timely returns to the ground station for recharging or battery swaps. In simulation, FLAME achieves 36% lower mission time compared to state-of-the-art. A high-fidelity simulation confirms the framework’s ability to effectively prioritise user-assigned regions while adhering to operational constraints.