The stability limits, the stabilization mechanism, and the flow field structure of highly stabilized partially premixed methane flames in a concentric flow conical nozzle burner with air co-flow have been investigated and presented in this work. The stability map of partial premixed flames illustrates that the flames are stable between two extinction limits. A low extinction limit when partial premixed flames approach non-premixed flame conditions, and a high extinction limit, with the partial premixed flames approach fully premixed flame conditions. These two limits showed that the most stable flame conditions are achieved at a certain degree of partial premixed. The stability is improved by adding air co-flow. As the air co-flow velocity increases the most stable flames are those that approach fully premixed. The turbulent flow field of three flames at 0, 5, 10 m/s co-flow velocity are investigated using Stereo Particle Image Velocimetry (SPIV) in order to explore the improvement of the flame stability due to the use of air co-flow. The three flames are all at a jet equivalence ratio (Φj) of 2, fixed level of partial premixing and jet Reynolds number (Rej) of 10,000. The use of co-flow results in the formation of two vortices at the cone exit. These vortices act like stabilization anchors for the flames to the nozzle tip. With these vortices in the flow field, the reaction zone shifts toward the reduced turbulence intensity at the nozzle rim of the cone. Interesting information about the structure of the flow field with and without co-flow are identified and reported in this work.