Combustion instability, which is the result of a coupling between combustor acoustic modes and unsteady flame heat release rate, is a severely limiting factor in the operability and performance of modern gas turbine engines. This coupling can occur through different coupling pathways, such as flow field fluctuations or equivalence ratio fluctuations. In realistic combustor systems, there are complex hydrodynamic and thermo-chemical processes involved, which can lead to multiple coupling pathways. In order to understand and predict the mechanisms that govern the onset of combustion instability in real gas turbine engines, we consider the influences that each of these coupling pathways can have on the stability and dynamics of a partially-premixed, swirl-stabilized flame. In this study, we use a model gas turbine combustor with two concentric swirling nozzles of air, separated by a ring of fuel injectors, operating at an elevated pressure of 5 bar. The flow split between the two streams is systematically varied to observe the impact on the flow and flame dynamics. High-speed stereoscopic particle image velocimetry, OH planar laser-induced fluorescence, and acetone planar laser-induced fluorescence are used to obtain information about the velocity field, flame, and fuel-flow behavior, respectively. Depending on the flow conditions, a thermoacoustic oscillation mode or a hydrodynamic mode, identified as the precessing vortex core, is present. The focus of this study is to characterize the mixture coupling processes in this partially-premixed flame as well as the impact that the velocity oscillations have on mixture coupling. Our results show that, for this combustor system, changing the flow split between the two concentric nozzles can alter the dominant harmonic oscillation modes in the system, which can significantly impact the dispersion of fuel into air, thereby modulating the local equivalence ratio of the flame. This insight can be used to design instability control mechanisms in real gas turbine engines.