This article studies the routing problem in a cognitive unmanned aerial vehicle (UAV) swarm (CU-SWARM), which employs the cognitive radio into a swarm of UAVs within a three-layer hierarchical aerial-ground integrated network architecture for emergency communications. In particular, the flexibly converged architecture utilizes a UAV swarm and a high-altitude platform to support aerial sensing and access, respectively, over the disaster-affected areas. We develop a -learning framework to achieve the intelligent routing to maximize the utility for CU-SWARM. To characterize the reward function, we take into account both the routing metric design and the candidate UAV selection optimization. The routing metric jointly captures the achievable rate and the residual energy of UAV. Besides, under the location, arc, and direction constraints, the circular sector is modeled by properly choosing the central angle and the acceptable signal-to-noise ratio for UAV to optimize the candidate UAV selection. With this setup, we further propose a low-complexity iterative algorithm using the dynamic learning rate to update -values during the training process for achieving a fast convergence speed. Simulation results are provided to assess the potential of the -learning framework of intelligent routing as well as to verify our overall iterative algorithm via the dynamic learning rate for training procedure. Our findings reveal that the proposed algorithm converges in a few number of iterations. Furthermore, the proposed algorithm can increase the accumulated rewards, and achieve significant performance gains, as compared to the benchmark schemes.