"any flower or plant growing in grain fields" (typically the common bluebottle), 1570s, from corn (n.1) + flower (n.).
Entries linking to cornflower
corn n.1
"grain," Old English corn "single seed of a cereal plant; seeds of cereal plants generally; plants which produce corn when growing in the field," from Proto-Germanic *kurnam "small seed" (source also of Old Frisian and Old Saxon korn "grain," Middle Dutch coren, German Korn, Old Norse korn, Gothic kaurn), from PIE root *gre-no- "grain."
The sense of the Old English word was "grain with the seed still in" (as in barleycorn) rather than a particular plant. Locally understood to denote the leading crop of a district. It has been restricted to the indigenous "maize" in America (c. 1600, originally Indian corn, but the adjective was dropped), usually "wheat" in England, "oats" in Scotland and Ireland, while Korn means "rye" in parts of Germany.
Maize was introduced to China by 1550, it thrived where rice did not grow well and was a significant factor in the 18th century population boom there. Corn-starch is from 1850. Corn-silk is attested from 1852.
flower n.
c. 1200, flour, also flur, flor, floer, floyer, flowre, "the blossom of a plant; a flowering plant," from Old French flor "flower, blossom; heyday, prime; fine flour; elite; innocence, virginity" (12c., Modern French fleur), from Latin florem (nominative flos) "flower" (source of Italian fiore, Spanish flor), from PIE root *bhel- (3) "to thrive, bloom."
From late 14c. in English as "blossoming time," also, figuratively, "prime of life, height of one's glory or prosperity, state of anything that may be likened to the flowering state of a plant." As "the best, the most excellent; the best of its or kind; embodiment of an ideal," early 13c. (of persons, mid-13c. of things); for example flour of milk "cream" (early 14c.); especially "wheat meal after bran and other coarse elements have been removed, the best part of wheat" (mid-13c.). Modern spelling and full differentiation from flour (n.) is from late 14c.
In the "blossom of a plant" sense it ousted its Old English cognate blostm (see blossom (n.)). Also used from Middle English as a symbol of transitoriness (early 14c.); "a beautiful woman" (c. 1300); "virginity" (early 14c.). Flower-box is from 1818. Flower-arrangement is from 1873. Flower child "gentle hippie" is from 1967.