The gradient of local equivalence ratio in reacting mixtures significantly affects the flame structure and their corresponding response to acoustic velocity perturbations. We study the effect of acoustic velocity fluctuations on flames created by two co-annular, swirling streams with different equivalence ratios to simulate the effects of pilot-mains split. The flames are stabilized both by a bluff body and by swirl. The flame responses were measured via chemiluminescence as a function of frequency, in the linear perturbation range. A linearized version of the G-equation model is employed to describe the flame dynamics, combined with effects of axial and azimuthal velocity perturbations downstream of the swirlers. The model accounts for the phase shift between the main acoustic and swirler vortical perturbations, which propagate at different speeds. The very different flame structures generated by different fuel splits lead to different flame responses. Models based on time delay of vortical disturbances are able to capture the behaviour reasonably well for the case of outer fuel enrichment, but offer limited agreement for the case of the inner enriched flame, particularly under higher mean equivalence ratios.