Combustion instability, characterized by self-sustained, large-amplitude pressure oscillations and periodic shedding of coherent vortex structures at varied spatial scales, has many detrimental effects on flight-propulsion dynamics and structural integrity of gas turbine engines. Hence, its early detection is one of the important tasks in engine health monitoring and prognostics. This paper proposes a dynamic data-driven approach, where a large volume of sequential hi-speed (greyscale) images is used to analyze the temporal evolution of coherent structures in combustion chamber for early detection of combustion instability at various operating conditions. The proposed hierarchical approach involves extracting low-dimensional semantic features from images using Deep Neural Networks followed by capturing the temporal evolution of the extracted features using Symbolic Time Series Analysis (STSA). Extensive experimental data have been collected in a swirl-stabilized dump combustor at various operating conditions for validation of the proposed approach. Intermediate layer visualization of deep learning reveals that meaningful shape-features from the flame images are extracted, which enables the temporal modeling layer to enhance the class separability between stable and unstable regions. At the same time, the semantic nature of intermediate features enables expert-guided data exploration that can lead to better understanding of the underlying physics. To the best of the authors knowledge, this paper presents one of the early applications of the recently reported Deep Learning tools in the area of prognostics and health management (PHM).