i haven't found anything specific about his age, but it is worth noting that he claims to know about the origins of the Hakurei Shrine.
well it not means that he lived back then
Huh? Rinnosuke, your face is all red, you know?Oh, it's nothing, rea—Whoa!? You're hot!!Wonder how many centuries it's been since I last caught a cold...Koff....... I sense this was just asking for a ridiculous misunderstanding.