A comparative study has been performed to investigate the flow instabilities and their interactions in a non-premixed methane jet flame using highly accurate numerical methods. The interaction between the jet flapping modes and buoyancy instability has been examined by comparing a full three-dimensional case and an idealised axisymmetric case, in order to identify the three-dimensional effects on the vortex dynamics. In addition, air co-flow flames have been numerically simulated to investigate the interaction between the shear and buoyancy instabilities. It was found that three-dimensional effects dominate the flame dynamics at downstream locations, where the flame exhibits transitional behaviour. The axisymmetric simulation is only able to capture the flow dynamics close to the jet nozzle exit. The air co-flow tends to stabilise the flame and to reduce the flame unsteadiness, which may also have an impact on the flickering frequency. Three-dimensional effects can greatly affect the strength of flame oscillation energy at downstream location, where the flapping modes enhance the flame unsteadiness. On the contrary, co-flow tends to reduce the strength of flame oscillation, especially at upstream locations.