The article investigates the responses of buoyant jet diffusion flames to the application of magnetic field gradients. In a magnetic gradient, the paramagnetic oxygen is submitted to a magnetic force of attraction directed to the center of the magnet. Positive and negative magnetic gradients effects were compared to the case with no applied magnetic field. Measurements in methane/air flames from a coaxial injector show that over a range of air coflow velocity, the magnetic gradients affect both the oxygen supply at the flame edge and the displacement of the vortices in the air side of the high temperature reaction zone. Upward increasing magnetic field attracts paramagnetic oxygen upwards leading to variations of the lift height and the flame length and counteracts the gravity convective motion attested by a noticeable decrease of the flickering frequency, whereas the upward decreasing magnetic field generates a downward magnetic force on oxygen, depriving the flame edge of oxygen attested by a higher lift height and enhancing the gravity convection in air along the flame evidenced by an increase of the flickering frequency. The flame visible luminosity is shown to be impacted by the magnetic field gradient effect that is related to the soot production through modifications of local temperature, stoichiometry, and residence time.