The combustion process in the scramjet engines generally takes place in unsteady conditions. The unsteadiness of the flame can be present locally or globally in supersonic combustion, for instance, reactant mixing, ignition, flame stabilization, and blow-off. Thus, unsteady supersonic combustion is an urgent problem that needs to be solved for real scramjet engine applications. This work helps to advance the knowledge of dual-mode scramjet combustion operating with different equivalence ratios by conducting quantitative analyses that characterize flame dynamics under flow separation. A hydrogen-fueled direct-injection scheme was computed using blastFoam code via large-eddy simulation of a scramjet test rig at a stagnation temperature of 950 K and a pressure of 0.82 MPa. The computational results were in good agreement with the experimental data, and two typical flame structures (cavity shear-layer and cavity assisted jet-wake stabilized flame) corresponding to the scram/ram operating modes were reproduced. The local flame structure and flow regime were investigated using a modified flame index and filter functions. A particular focus was set on the continuous flame flashback during mode transition, which could be divided into three stages involving jet/shear-layer interaction, unsteady heat release, and the establishment of a large-area separation zone, with the decay of the cavity recirculation zone. Additionally, the unsteady jet-wake ram combustion presented three oscillation modes, giving rise to intermittent flameout of varying levels. The coherent-structures motion caused by the combined effects of low-speed separated flow and the fuel-jet was the main cause for this kind of unsteady combustion.