Unmanned Aerial Vehicles (UAVs) require robust navigation in dynamic environments to avoid collisions with non-cooperative obstacles like birds or other aerial objects, whose trajectories are non-linear, irregular, and not governed by road or air-traffic rules. Data-driven forecasting models such as Recurrent Neural Networks (RNNs) and Transformers, have shown strong performance in trajectory forecasting; however, progress in the UAV domain is constrained by the absence of publicly available data capturing such unstructured aerial motions. In this paper, we present SynTraG, a parametric synthetic trajectory generator that produces a configurable and extensive corpus of 3D trajectories by mixing kinematic primitives that emulate common non-cooperative motions: linear flight, oscillatory weaving, complex looping maneuvers, and vertical undulations. The generator is formulated as a mixture of closed-form kinematic primitives with randomized parameters and explicit controls over path length, speed, acceleration, curvature, and spectral content. Heteroscedastic Gaussian noise is incorporated to model localization uncertainty (e.g., GPS/IMU errors) to enable probabilistic trajectory forecasting. We provide an open-source implementation of SynTraG and a sample dataset of 47,894 diverse trajectories, which enables robust training and benchmarking of forecasting models for UAV collision avoidance with non-cooperative dynamic obstacles. This work enables the development and standardized benchmarking of next-generation forecasting models for safer autonomous aerial navigation.