Flame dynamics and combustion instability is a complex problem involving different non-linearities. Combustion instability has several detrimental effects on flight-propulsion dynamics and structural integrity of gas turbines and any such spaces where combustion takes places internally, primarily in internal combustion engines. The description of coherent features of fluid flow in such cases is essential to our understanding of the flame dynamics and propagation processes. A method that is able to extract dynamic information from flow fields that are generated by a direct numerical simulation or visualized in a physical experiment (like in the case discussed in this paper) is Dynamic Mode Decomposition. This paper presents such a feature extraction and stability analysis of hi-speed combustion flames using Dynamic Mode Decomposition and it's sparsity promoting variant. Extensive experimental data was collected in a swirl-stabilized dump combustor at various operating conditions (e.g. premixing level and flow velocity) for analysing the flame stability conditions. Copyright © 2016 by ASME.