Multiple unmanned aerial vehicles (UAVs) are able to efficiently accomplish a variety of tasks in complex scenarios. However, developing a collision-avoiding flocking policy for multiple fixed-wing UAVs is still challenging, especially in obstacle-cluttered environments. In this article, we propose a novel curriculum-based multiagent deep reinforcement learning (MADRL) approach called task-specific curriculum-based MADRL (TSCAL) to learn the decentralized flocking with obstacle avoidance policy for multiple fixed-wing UAVs. The core idea is to decompose the collision-avoiding flocking task into multiple subtasks and progressively increase the number of subtasks to be solved in a staged manner. Meanwhile, TSCAL iteratively alternates between the procedures of online learning and offline transfer. For online learning, we propose a hierarchical recurrent attention multiagent actor-critic (HRAMA) algorithm to learn the policies for the corresponding subtask(s) in each learning stage. For offline transfer, we develop two transfer mechanisms, i.e., model reload and buffer reuse, to transfer knowledge between two neighboring stages. A series of numerical simulations demonstrate the significant advantages of TSCAL in terms of policy optimality, sample efficiency, and learning stability. Finally, the high-fidelity hardware-in-the-loop (HITL) simulation is conducted to verify the adaptability of TSCAL. A video about the numerical and HITL simulations is available at https://youtu.be/R9yLJNYRIqY.