Many industrial combustion systems, especially power generation gas turbines, use fuel-lean combustion to reduce NOx emissions. However, these systems are highly susceptible to combustion instability, the coupling between combustor acoustics and heat release rate oscillations of the flame. It has been shown in previous work by the authors that a precessing vortex core (PVC) can suppress shear layer receptivity to external perturbations, reducing the potential for thermoacoustic coupling. The goal of this study is to understand the effect of combustor exit boundary condition on the flow structure of a swirling jet to increase fundamental understanding of how combustor design impacts PVC dynamics. The swirling jet is generated with a radial-entry, variable-angle swirler, and a quartz cylinder is fixed on the dump plane for confinement. Combustor exit constriction plates of different diameters are used to determine the impact of exit boundary condition on the flow field. Particle image velocimetry (PIV) is used to capture the velocity field inside the combustor. Spectral proper orthogonal decomposition, a frequency-resolved eigenvalue decomposition that can identify energetic structures in the flow, is implemented to identify the PVC at each condition in both energy and frequency space. We find that exit boundary diameter affects both the structure of the flow and the dynamics of the PVC. Higher levels of constriction (smaller diameters) force the downstream stagnation point of the vortex breakdown bubble upstream, resulting in greater divergence of the swirling jet. Further, as the exit diameter decreases, the PVC becomes less energetic and less spatially defined. Despite these changes in the base flow and PVC coherence, the PVC frequency is not altered by the exit boundary constriction. These trends will help inform our understanding of the impact of boundary conditions on both static and dynamic flame stability.