In this paper, a novel framework is proposed to perform data-driven air-to-ground (A2G) channel estimation for millimeter wave (mmWave) communications in an unmanned aerial vehicle (UAV) wireless network. First, an effective channel estimation approach is developed to collect mmWave channel information, allowing each UAV to train a stand-alone channel model via a conditional generative adversarial network (CGAN) along each beamforming direction. Next, in order to expand the application scenarios of the trained channel model into a broader spatial-temporal domain, a cooperative framework, based on a distributed CGAN architecture, is developed, allowing each UAV to collaboratively learn the mmWave channel distribution in a fully-distributed manner. To guarantee an efficient learning process, necessary and sufficient conditions for the optimal UAV network topology that maximizes the learning rate for cooperative channel modeling are derived, and the optimal CGAN learning solution per UAV is subsequently characterized, based on the distributed network structure. Simulation results show that the proposed distributed CGAN approach is robust to the local training error at each UAV. Meanwhile, a larger airborne network size requires more communication resources per UAV to guarantee an efficient learning rate. The results also show that, compared with a stand-alone CGAN without information sharing and two other distributed schemes, namely: A multi-discriminator CGAN and a federated CGAN method, the proposed distributed CGAN approach yields a higher modeling accuracy while learning the environment, and it achieves a larger average data rate in the online performance of UAV downlink mmWave communications.