eat
啖 centers on the act of eating, with a nuance of consuming or devouring.
啖 combines 口 (mouth) with 炎, which likely contributes the sound and may suggest the heat of devouring food. The exact historical development is uncertain.
A mouth 口 beside flames 炎: picture someone eating fiery hot food, devouring it eagerly.
For タン, imagine a tanuki (たぬき) eating greedily: tanuki -> タン, and the tanuki's mouth is devouring everything.