We report on a study of the impact of coherent helical vortex structures on the shape of the reaction zone and heat release in swirling methane/air flames in regimes with a vortex breakdown. Three kinds of atmospheric flames are considered, viz., fuel-lean and fuel-rich premixed flames and a partially premixed fuel-rich lifted flame. Based on the measurements of the velocity fields by a stereo PIV in combination with the OH PLIF and HCHO PLIF, the impact of the coherent flow structures on large-scale corrugations of the reaction zone is evaluated. Helical vortex structures, detected in both the non-reacting and reacting high-swirl flows by using proper orthogonal decomposition, are found to promote combustion both in the lean premixed and fuel-rich partially premixed flames. In the first case, based on the phase-averaged intensity of the HCHO×OH signal and the location of the helical vortex structure in the inner mixing layer, it is concluded that the vortex locally increases the heat release rate by enlarging the flame front and enhancing the mass exchange between the combustion products inside the recirculation zone and the fresh gases. The events of the local flame extinctions are detected in the instantaneous PLIF snapshots for the lean mixture, but they do not cause extinction of the entire flame or a blow-off. In case of the lifted flame, the outer helical vortex structure promotes combustion by locally intensifying the mass exchange between the fuel-rich jet with the surrounding air.