The Flap Control System (FCS) is a critical component of jet airplanes, designed to increase lift and reduce takeoff and landing roll distances. Malfunctions in the FCS, particularly Trailing Edge Flap (TEF) asymmetry failures, pose significant safety risks, potentially leading to delays or emergency landings. Comprehensive and efficient monitoring is essential, yet conventional fault diagnosis methods based on TEF angle trends lack predictability and speed due to the complexity of such faults. This paper proposes a data-driven approach for diagnosing and predicting TEF asymmetry failures in the Boeing B737NG FCS. Leveraging large-scale flight data from Quick Access Recorders (QAR), a baseline mining model using the LightGBM algorithm is developed to process high-dimensional data and model deflection angles dynamically. Based on this, a dynamic deflection angle threshold and The Asymmetry Index (TAI) are constructed, followed by diagnostic and prognostic experiments. The results demonstrate that the proposed method captures FCS dynamics more effectively than fixed-threshold approaches, proving its utility in diagnosing and predicting TEF asymmetry failures. These findings highlight the potential of data-driven approaches for FCS monitoring and emphasize the advantages of dynamic thresholds and TAI in improving fault detection and prediction.