The authors analyzed the behavior of a laminar CH4/air flame with a central methane jet and surrounding air jet in a large range of fuel and air flow rates. Different regimes of flame stability are observed from an anchored flame to a stable lifted flame, which is destabilized before extinction. It is shown that the flame instabilities are coupled to the production of vortices on the air jet/ambient air side and is depending on the injected air velocity. Influence of an upward increasing magnetic field is studied by setting the flame inside the bore of an electromagnet. Measurements at different values of methane and air flow rates show that the flame liftoff height is decreased by the magnetic gradient. It is attributed to the magnetic force, which develops on air via its action with paramagnetic oxygen. The magnetic force interacts with the air jet structures and influences the flame stability.