Lampadomancy
Lampadomancy (Greek lampas, lamp) is divination by observing the flame of an oil lamp. Practice attested in ancient Egypt and Greece. Variation of velomancy (candle divination), but with oil lamp — distinct fuel produces different flame behavior.
Reading
Strong stable flame = approval; flame that flickers = doubt; sudden extinction = bad omen; flame that splits = dilemma; sparks = unexpected news.