Etymology
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flan (n.)
"open tart," 1846, from French flan "custard tart, cheesecake," from Old French flaon "flat-cake, tart, flan" (12c.), from Medieval Latin flado (10c.), which probably is from Frankish *flado or another Germanic source (compare Old High German flado "offering cake," Middle High German vlade "a broad, thin cake," Dutch vla "baked custard"), from Proto-Germanic *flatho(n) "flat cake," which is probably from PIE root *plat- "to spread." Borrowed earlier as flawn (c. 1300), from Old French.
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*plat- 

also *pletə-, Proto-Indo-European root meaning "to spread;" extension of root *pele- (2) "flat; to spread."

It forms all or part of: clan; flan; flat (adj.) "without curvature or projection;" flat (n.) "a story of a house;" flatter (v.); flounder (n.) "flatfish;" implant; piazza; place; plaice; plane; (n.4) type of tree; plant; plantain (n.2); plantar; plantation; plantigrade; plat; plate; plateau; platen; platform; platinum; platitude; Platonic; Plattdeutsch; platter; platypus; plaza; supplant; transplant.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit prathati "spreads out;" Hittite palhi "broad;" Greek platys "broad, flat;" Latin planta "sole of the foot;" Lithuanian platus "broad;" German Fladen "flat cake;" Old Norse flatr "flat;" Old English flet "floor, dwelling;" Old Irish lethan "broad."

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flank (n.)
late Old English flanc "flank, fleshy part of the side," from Old French flanc "hip, side," from Frankish or another Germanic source, from Proto-Germanic *hlanca- (source also of Old High German (h)lanca, Middle High German lanke "hip joint," German lenken "to bend, turn aside;" Old English hlanc "loose and empty, slender, flaccid;" Old Norse hlykkr "a bend, noose, loop"), from PIE root *kleng- "to bend, turn" (see link (n.)). Showing characteristic change of Germanic hl- to Romanic fl-. The military sense is first attested 1540s. Meaning "side" of anything is by 1620s. As an adjective, "pertaining to the flank or side," 1660s. Related: Flanked; flanking.
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Flanders 
from a source akin to Dutch Vlaanderen probably a compound of roots represented by Flemish vlakte "plain" + wanderen "to wander."
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flaneur (n.)

"habitual loafer, idle man about town," 1854, from French flâneur, from flâner "to stroll, loaf, saunter," probably from a Scandinavian source (compare Old Norse flana "to wander aimlessly," Norwegian flana, flanta "to gad about"), perhaps from PIE root *pele- (2) "flat; to spread." Related: flânerie.

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flange (n.)
1680s, "a widening or branching out," of unknown origin, perhaps related to Old French flanche "flank, hip, side," fem. of flanc (see flank (n.)). Meaning "projecting rim, etc., used for strength or guidance" is from 1735. As a verb from 1820.
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flannel (n.)
"warm, loosely woven woolen stuff," c. 1300, flaunneol, probably related to Middle English flanen "sackcloth" (c. 1400); by Skeat and others traced to Welsh gwlanen "woolen cloth," from gwlan "wool," from Celtic *wlana, from PIE *wele- (1) "wool" (see wool). "As flannel was already in the 16th c. a well-known production of Wales, a Welsh origin for the word seems antecedently likely" [OED].

The Welsh origin is not a universally accepted etymology, due to the sound changes involved; Barnhart, Gamillscheg, Diez suggest the English word is from an Anglo-French diminutive of Old French flaine "a kind of coarse wool." Modern French flanelle is a 17c. borrowing from English.
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flank (v.)
1590s (military), "to guard the flank," also, "to menace the flank, fire sideways upon," from flank (n.). Meaning "stand or be placed at the side of" is from 1650s. Related: Flanked; flanking.
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arrow (n.)

"slender, pointed missile weapon, made to be shot from a bow," early 14c., from Old English arwan, earlier earh "arrow," possibly borrowed from Old Norse ör (genitive örvar), from Proto-Germanic *arkhwo (source also of Gothic arhwanza), from PIE root *arku-, source of Latin arcus (see arc (n.)). The etymological sense would be "the thing belonging to the bow." The meaning "a mark like an arrow" in cartography, etc. is from 1834.

It was a rare word in Old English. More common words for "arrow" were stræl (which is cognate with the word still common in Slavic and once prevalent in Germanic, related to words meaning "flash, streak") and fla, flan (the -n perhaps mistaken for a plural inflection), from Old Norse, a North Germanic word, perhaps originally with the sense of "splinter." Stræl disappeared by 1200; fla became flo in early Middle English and lingered in Scottish until after 1500.

Robyn bent his joly bowe,
Therein he set a flo.
["Robyn and Gandelyn," in a minstrel book from c. 1450 in the British Museum]
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