The stability and control derivatives of an unmanned aerial vehicle (UAV) map the platform's control inputs to its dynamic response. The modeling is labor intensive and requires coarse approximations. Similarly, models constructed through flight tests are only applicable to a narrow flight envelope, and classical system identification approaches require prior knowledge of the model structure, which, in some instances, may only be partially known. The goal of this study is to tackle these problems by introducing a new system identification method based on the dependent Gaussian processes. This allows high-fidelity nonlinear flight dynamic models to be constructed through experimental data. The proposed algorithm captures the cross coupling between input parameters and learns the system stability and control derivatives. In addition, it captures any dependences embodied in the outputs. This paper provides both the theoretical underpinnings and practical application of this approach. The theory was tested in simulation on a highly coupled oblique wing aircraft and was demonstrated on a delta-wing UAV platform using real flight data. The results are compared against an alternative parameteric model and show improvements in identifying the coupling between flight modes, the ability to provide uncertainty estimates and robustness, and applicability to a broader flight envelope.