The relation between flow field and flame structure of a turbulent swirl flame is investigated using simultaneous particle image velocimetry (PIV) and planar laser-induced fluorescence of OH (OH-PLIF). The measurements are performed in one axial and three transverse sections through the combustion chamber of a gas turbine model combustor, which is operated with methane and air under atmospheric pressure. Analysis of the velocity fields using proper orthogonal decomposition (POD) shows that the dominant unsteady flow structure is a so-called precessing vortex core (PVC). In each of the four sections, the PVC is represented by a characteristic pair of POD eigenmodes, and the phase angle of the precession can be determined for each instantaneous velocity field from its projection on this pair. Phase-conditioned averages of velocity field and OH distribution are thereby obtained and reveal a pronounced effect of the PVC in the form of convection-enhanced mixing. The increased mixing causes a rapid ignition of the fresh gas, and the swirling motion of the PVC leads to an enlarged flame surface due to flame roll-up. A three-dimensional representation shows that the PVC is accompanied by a co-precessing vortex in the outer shear layer, which, however, has no direct impact on the flame. As an alternative to phase averaging, a low-order representation of the phase-resolved dynamics is calculated based on the first pair of POD modes. It is found that small-scale structures are represented more accurately in the phase averages, whereas the low-order model has a considerable smoothing effect and therefore provides less detailed information. The findings demonstrate that the combined application of POD, PIV, and PLIF can provide detailed insights into flow–flame interaction in turbulent flames.