1756, probably imitative of the sound made by something brushing against or through something. Related: Swished; swishing.
1820, from swish (v.); sense of "effeminate homosexual" is 1930s in homosexual slang, probably from notion of mincing motion.
Showing the traits of an effeminate male homosexual; mincing; limp-wristed, nellie: His walk was quite swish (1930s+ Homosexuals)
nounTo move, walk, speak, etc, in the manner or presumed manner of effeminate male homosexuals (fr homosexuals)
[perhaps fr the swinging movements of the hips in a mincing walk; perhaps fr swish2]