Combustion stability is an important consideration for many energy systems because of its impact on performance and efficiency. Flame dynamics that govern combustion stability are often complex and difficult to resolve, particularly from experimental data. However, recent advances in postprocessing techniques, such as dynamic mode decomposition (DMD), have partially enabled flame dynamic analysis. This study aims to provide a comprehensive measure of combustion stability through a detailed investigation of coherent structures and their energy contents, frequencies, and growth factors from DMD. These results are then correlated to underlying physics and chemistry that drive flame dynamics. Three different data sets were analyzed in this study. Numerically constructed images and OH-planar laser induced fluorescence (OH-PLIF) images of laminar flames were used to characterize stable flame dynamics. OH-PLIF images of acoustically perturbed swirl-stabilized turbulent flames were used to characterize oscillatory and unstable flame dynamics. Acoustic perturbation at various frequencies and amplitudes were introduced using a speaker. Dominant spatial structures and their energy contents in the recirculation zone or shear layer were accurately resolved. Frequencies and growth factors provided good mode-specific stability assessment. Overall, the stability analysis is an effective technique for analyzing flame dynamics and developing more stable combustion systems despite complex interaction between acoustics, fluid mechanics, and combustion.