The Black Flan, also known as the SLIME in the NES version and Dark Flan in the PS version, is an enemy in the original Final Fantasy. Its phenomenal Defense stat renders physical attacks ineffective against it, so a multi-targeted Firaga works best. It is located in the Flying Fortress on the bridge leading to Tiamat.
Its Japanese name most likely refers to the "Black Pudding" monster in Dungeons & Dragons. Flan is an open pastry or sponge cake containing a sweet or savory filling. A typical flan of this sort is round, with shortcrust pastry, usually coated with sweet syrup. It is similar to a custard tart or a South African melktert.