The Law of Conservation of Mass states that mass could not be created or destroyed.
Burning, in fact, is a vigorous oxidation process. During burning, the substance combines with oxygen from the air forming compounds. Depending on the material nature of the substance, most of the compounds so formed are gases, (such as carbon dioxide, sulphur dioxide, nitrous oxides...etc.) and would be escape away in the air. That's why you observe that a substance looks to "disppear" after burning.
In the actual sense, if you could collect all the gases evolved during burning, you would find that the mass of which is larger than that of the substacne before burning. It is because of the addition of the mass of oxygen involved in the burning process.