"flat end of an arm of an anchor," 1560s, perhaps from fluke (n.3) on resemblance of shape, or from Low German flügel "wing." Meaning "whale's tail" (in plural, flukes) is 1725.
"lucky stroke, chance hit," 1857, originally a lucky shot at billiards, of uncertain origin.
"flatfish," Old English floc "flatfish," related to Old Norse floke "flatfish," flak "disk, floe" (see flake (n.)). The parasite worm (1660s) so called from resemblance of shape.
fluke 1 (flōōk)
A good or bad stroke of luck; an extraordinary and unpredictable event: My winning was just a fluke/ We got onto that flight by a fluke
[1857+; origin unknown, but perhaps fr fluke, ''flatfish,'' by way of an early 1800s British slang sense of flat, ''easy dupe, victim,'' altered in billiards jargon to fluke, to characterize the seeming chicanery of a good stroke of luck]