Toward the goal of understanding and controlling instability in combustion systems, we present a fundamental characterization of the interaction of the buoyancy-induced instability in flickering flames with forced excitation of fuel supply. Laminar coflow diffusion flames were acoustically forced, whose frequency responses were recorded as a function of excitation frequency and amplitude. The evolving structure of such flames was also examined through the use of video analysis and particle imaging velocimetry (PIV). For specific combinations of excitation frequency and amplitude, the frequency response of the flames was found to couple to that of the forcing, where the contribution of natural puffing frequency disappears. Such instances of coupling exhibited many harmonics of the excitation frequency, related indirectly to the natural puffing frequency. We showed how such harmonics form, through application of PIV, and furthermore unveiled insight into the physics of how the flame couples to the forcing under certain conditions. Our frequency response characterization provides quantitative results, which are of utility for both modeling studies and active-control strategies.