The paper investigates the dynamics of methane – oxygen enriched air turbulent non-premixed swirled flames and their emission characteristics. The burner configuration consists of two concentric tubes with a swirler placed in the annular part supplying the oxidant. Fuel injection is radial through holes in the central tube at the burner exit. This allows enhancing air-fuel mixing and eases flame stabilisation. Fuel is injected into the highest turbulence level regions where the local mixing is enhanced, and generating a shift from a non-premixed flame towards a partially premixed one. The idea of oxygen enrichment of the air is related to the augmentation of CO$_2$ concentration in the flue gases to improve the CO$_2$ capture efficiency by membranes. Stereo-Particle Image Velocimetry is used to analyse the velocity flow fields. The measurements are performed for oxygen concentrations ranging from 21% to 30%, with swirl numbers from 0.8 to 1.4 and global equivalence ratio from 0.8 to 1. Results show that combustion noticeably affects the swirling motion and that tangential velocities rapidly decrease along the axial axis. The recirculation mass flow ratio dramatically increases compared to non-reactive cases. Increasing global equivalence ratios increases the recirculation mass flow ratio contrary to oxygen enrichment effects. The exhaust gas compositions are measured using gas analysers. It is observed that NO$_x$ emissions decrease when the global equivalence ratio increases. It suggests that CO$_2$ in the recirculated burned gases could be responsible for NO$_x$ destruction at relatively high oxygen enrichment rates. Globally, the results show that, by combining enhanced mixing and moderate oxygen enrichment of the air, the developed and characterized new burner configuration has a good potential to be used to stabilize non-premixed fuel and oxidant streams as partially premixed low emission flames with an increased concentration of CO$_2$ in the flue gases.