Truth be told, the earliest record of fly fishing was dapping which is the basis of Tenkara.
The earliest account of what could be interpreted as fly fishing is from 200 AD.
"They fasten red (crimson red) wool around a hook, and fix onto the wool two feathers which grow under a cock’s wattles, and which in colour are like wax. Their rod is six feet long, and their line is the same length. Then they throw their snare, and the fish, attracted and maddened by the colour, comes straight at it, thinking from the pretty sight to gain a dainty mouthful; when, however, it opens its jaws, it is caught by the hook, and enjoys a bitter repast, a captive."
Fly Fishing History: Ælian
So this is not a recent form of fly fishing but the earliest form of fly fishing. Casting a fly line is not mentioned until about 1500 years later.