I’m sure the Romans fly fished, but thier techniques was different. They would catch a fly and drop it on the water. When a fish came up to grab it, they would skewer it with those short Gladius swords, hence the term Et Fillet, et Spiritu Sancto…
Seriously, I don’t think they fly-fished themselves, but merely reported on other peoples that did it, like the Macedoneans.