Safety, as the most important concern in civil aviation, needs to be maintained at an acceptable level at all times in the air transportation system. This paper aims to increase en-route flight safety through the development of deep learning models for trajectory prediction, where model prediction uncertainty is characterized following a Bayesian approach. The proposed methodology consists of four steps. In the first step, a large volume of raw messages in Flight Information Exchange Model (FIXM) format streamed from Federal Aviation Administration are processed with a distributed computing engine Apache Spark to extract trajectory information in an efficient manner. In the second step, two types of deep learning models are trained to predict flight trajectory from different perspectives. Specifically, deep feedforward neural networks (DNN) are trained to make a one-step-ahead prediction on the deviation along latitude and longitude between the actual flight trajectory and target flight trajectory. In parallel, deep Long Short-Term Memory (LSTM) neural networks are trained to make longer-term predictions on the flight trajectory over several subsequent time instants. The DNN model is more accurate but has a single-step prediction horizon, whereas the LSTM model is less accurate but longer prediction horizon. Therefore, in the third step, the two different types of deep learning models are blended together to create a multi-fidelity prediction. After quantifying the discrepancy between the two model predictions in the current time instant, the DNN prediction is used to correct the LSTM prediction of flight trajectory along subsequent time instants accordingly. The multi-fidelity approach is expanded to multiple flights, and is then used to assess safety based on horizontal and vertical separation distance between two flights. Computational results illustrate the promising performance of the blended model in predicting the flight trajectory and assessing en-route flight safety.