A multi-fidelity deep learning-based model is developed in this paper to make predictions on the trajectory of an ongoing flight by learning from the patterns embodied in its historical trajectory data streamed from System Wide Information Management (SWIM) Flight Data Publication Service (SFDPS). The proposed method is illustrated with a four-step procedure. In the first step, a fast and scalable big data engine – Apache Spark – is leveraged to parse the massive raw flight tracking messages in XML format, filter flight position data, correlate flight tracking messages with the corresponding flight ID in an effective manner. In the second step, we build two individual deep learning models to predict the future state of flight trajectory from different perspectives. Specifically, a deep feedforward neural network (DNN) is trained to make one-step-ahead predictions on the latitude and longitude deviation between the actual flight trajectory and target flight trajectory. In parallel, a deep Long Short-Term Memory (LSTM) neural network is trained to make longer-term predictions on the flight trajectory over multiple subsequent time instants. The prediction uncertainties in both deep learning models are characterized following a Bayesian approach. In the third step, LSTM prediction is corrected using the more accurate DNN prediction, thus achieving both accuracy and computational efficiency. Finally, the multi-fidelity approach is extended to multiple flights, then we use separation distance as a quantitative metric to measure the en-route safety between any two flights. Numerical examples are used to demonstrate the effectiveness of the proposed methodology.