On Earth, the hot gases from the flame rise upward and draw more oxygen into the flame to keep it burning. This is because the hot gases are lighter than the surrounding air. But this depends on gravity. With no gravity, these burned gases would remain around the flame, and block any more oxygen from reaching it. And thus any naked flame will be snuffed out.
Oh well. In my above answer, just replace the word 'gravity' with 'gravitational effect'. (I didn't see any point in going into explanations of 'inertial frames', Jake!)
No no one is going to let you try this! but if you had a long enough 'throughway' on the ISS and you could get the candle moving in a straight line and then lit it, you might be able to replenish the oxygen fast enough from the front, leaving the combustion products behind. Come to think of it, just stand next to one of the air-conditioning air inlets - that would probably do the trick.