Video data from experiments on the dynamics of two-dimensional flames are analyzed. The Karhunen-Loéve (KL) analysis is used to identify the dominant spatial structures and their temporal evolution for several dynamical regimes of the flames. A data analysis procedure to extract and process the boundaries of flame cells is described. It is shown how certain spatial structures are associated with certain temporal events. The existence of small scale, high frequency, turbulent background motion in almost all regimes is revealed.