From Middle English flake, from Old English flacca and/or Old Norse flak (compare Old Norse flakna), from Proto-Germanic *flaką, from Proto-Indo-European *pleh₂- ("flat, broad, plain"). Cognate with Norwegian flak ("slice, sliver"), Swedish flak ("a thin slice"), Danish flage ("flake"), German Flocke ("flake"), Dutch vlak ("smooth surface, plain") and vlok, Latin plaga ("flat surface, district, region"). plage.
A name given to dogfish to improve its marketability as a food, perhaps from etymology 1.