Gaussian Processes (GPs) are expressive models for capturing signal statistics and expressing prediction uncer-tainty. As a result, the robotics community has gathered interest in leveraging these methods for inference, planning, and control. Unfortunately, despite providing a closed-form inference solution, GPs are non-parametric models that typically scale cubically with the dataset size, hence making them difficult to be used especially on onboard Size, Weight, and Power (SWaP) constrained aerial robots. In addition, the integration of popular libraries with GPs for different kernels is not trivial. In this paper, we propose GaPT, a novel toolkit that converts GPs to their state space form and performs regression in linear time. GaPT is designed to be highly compatible with several optimizers popular in robotics. We thoroughly validate the proposed approach for learning quadrotor dynamics on both single and multiple input GP settings. GaPT accurately captures the system behavior in multiple flight regimes and operating conditions, including those producing highly nonlin-ear effects such as aerodynamic forces and rotor interactions. Moreover, the results demonstrate the superior computational performance of GaPT compared to a classical GP inference approach on both single and multi-input settings especially when considering large number of data points, enabling real-time regression speed on embedded platforms used on SWaP-constrained aerial robots.