Light both candles. Add vinegar to the baking soda. If the flame needs oxygen, the flame should be extinguished in the baking soda jar because the carbon dioxide produced when the vinegar is added will force the oxygen out. Since carbon dioxide is heavier than oxygen, the carbon dioxide will stay in the bottom of the jar. The demonstration could be repeated using dry ice.
Dry ice is solid carbon dioxide.
Great caution needs to be taken when using dry ice. Inflate one bag by blowing into it. At the same time, inflate the other bag by opening up and pulling through the air. Carefully place both bags over the candles at the same time. Since the breathed-in bag will contain less oxygen, the candle in that bag will stop burning first.