The analysis of the interaction between the swirling and cooling flows, promoted by the liner film cooling system, is a fundamental task for the design of turbine combustion chambers since it influences different aspects such as emissions and cooling capability. In particular, high turbulence values, flow instabilities, and tangential velocity components induced by the swirling flow deeply affect the behavior of effusion cooling jets, demanding for dedicated time-resolved near-wall experimental analysis. The experimental setup of this work consists of a non-reactive single sector linear combustor test rig scaled up with respect to engine dimensions; the test section was equipped with an effusion plate with standard inclined cylindrical holes to simulate the liner cooling system. The rig was instrumented with a 2D time-resolved particle image velocimetry system, focused on different field of views. The degree of swirl for a swirling flow is usually characterized by the swirl number, Sn, defined as the ratio of the tangential momentum flux to axial momentum flux. To assess the impact of such parameter on the near-wall effusion behavior, a set of three different axial swirlers with swirl number equal to Sn = 0.6–0.8–1.0 were designed and tested in the experimental apparatus. An analysis of the main flow field by varying the Sn was first performed in terms of average velocity, root mean square, and Tu values, providing kinetic energy spectra and turbulence length scale information. In a second step, the analysis was focused on the near-wall regions: the strong effects of Sn on the coolant jets were quantified in terms of vorticity analysis and jet oscillation.