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Above the fire, the temperature of the atmosphere is higher. And as we know that at constant  pressure, the density and temperature is inversely related, so the density above the fire is decreased.
While looking beyond the fire, line of sight have to cross that low density location, because of that the objects seen swaying.
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They appear swaying because above the fire there is very less denser air which cause the ray of the light to refract and because of refraction of every ray of light which is coming from the object through that less denser air they appear swaying.
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