The present paper reports on planar optical measurements of coherent structures in a swirling jet with vortex breakdown and combustion. Two configurations of the atmospheric propane/air swirling flames are considered, namely, fuel-lean premixed and fuel-rich partially premixed flames. Deformations of the flame front are visualized by planar laser-induced fluorescence (PLIF) of HCHO. The instantaneous velocity fields are measured by particle image velocimetry (PIV). For extraction of coherent structures from the data sets, they are processed by proper orthogonal decomposition (POD). The instantaneous PLIF snapshots showed that the flame fronts were strongly corrugated by turbulent fluctuations. The POD analysis of both PIV and PLIF data sets revealed spatial modes of large-scale deformations of the reaction zone. From the analysis of the PIV data it was found that these modes were caused by two different types of hydrodynamics flow instabilities. One of them corresponded to large-scale vortex structures due to centrifugal instability of the swirling jet flow and breakdown of the vortex core. Another mode was related to unsteady longitudinal velocity fluctuations caused by the upward plume oscillations driven by buoyancy effect.