As we know when sodium bicarbonate (baking powder) and acetic acid (the vinegar) react, carbon dioxide (a gas) is released.
Since carbon dioxide is a gas, as the quantity of gas increases, likely does its volume (PV=nRT). The reaction of vinegar with baking powder, can fill a balloon as carbon dioxide is released from the reaction.
This is movie about the functioning of carbon dioxide fire extinguishers. If oxygen is removed by a gas that isn't combustive then the combustion reaction comes to an end.