Camouflage was made famous by painters in uniform, but the word itself began as French slang. One likely influence on it is a prank involving smoke blown up a sleeping person's nose.
The war came first. In September 1914, Lucien-Victor Guirand de Scévola was a second-class gunner in the French artillery. Before the war he had been a Paris-trained painter known for silky pastel portraits. At the front he hid a gun position behind a painted canvas screen.
On 12 February 1915, General Joffre set up a Section de Camouflage at Amiens. By the end of the year De Scévola was in charge. By 1917 his team had grown to 3,000, including artists such as Jacques Villon and André Mare. De Scévola openly borrowed from modern art. "In order to deform totally the aspect of an object," he said, "I had to employ the means that cubists use to represent it." His workers were known as camoufleurs.
English took the word quickly. Etymonline dates it to 1917 and quotes Popular Science Monthly from August that year: "Until recently there was no one word in any language to explain this war trick." Britain's navy used its own term for its painted ships, "dazzle-painting." Merriam-Webster does record an earlier English noun, from 1885, in the general sense of concealment by disguise. The war is what made it common.
The French word is camoufler, "to disguise," plus the noun ending -age. Merriam-Webster says camoufler was originally criminal slang. Etymonline calls it Parisian slang and traces it to Italian camuffare, "to disguise." The Italian word's own origin is uncertain, perhaps capo muffare, "to muffle the head."
Both dictionaries point to a second influence: camouflet. Merriam-Webster defines it as a practical joke in which a paper cone is set alight and its smoke blown into the nose of a sleeping person. Etymonline glosses it more simply as "puff of smoke." Merriam-Webster traces camouflet to Middle French chault moufflet, with chault meaning "warm," from Latin calidus.
Nobody can map the exact route from smoke prank to military art. But the idea fits: both blind the other side, if only for a moment.