The word "fly" for fold of cloth for closure of trousers originated long before zippers were invented.

Indeed so, as confirmed by an old limerick:
.....There was a young girl of Darjeeling
.....Who could dance with such exquisite feeling
.....Not a murmur was heard,
.....Not a sound not a word,
.....Save the fly-buttons hitting the ceiling.

The zipper was first exhibited at the 1893 Chicago World's Fair, but it was largely ignored and impractical. (The postal service ordered a few zipper mail bags, but the zippers jammed so frequently that the bags were discarded.) The U.S. Army used an improved zipper design on clothing and equipment during World War I. At the time the zipper was principally a closure for boots, given the manufacturing difficulty of producing a functional zipper small enough for use on other clothing. It did not became a common clothing fastener until the late 1920's, and in 1935 became a fashion craze, with clothing decorated with zippers that were colorful, decorative and completely non-functional.

Whence the word zipper? In 1923 B. F. Goodrich Company (now a major producer of tires) came out with rubber galoshes with a zipper closure. Mr. Goodrich himself coined the word zipper as an echoic name, from the zip sound the zippers made.