I honestly don't know how you define archaic here because it's very much a current usage of the word.

(of a linguistic form) commonly used in an earlier time but rare in present-day usage except to suggest the older time, as in religious rituals or historical novels. Examples. thou; wast; methinks; forsooth.

Its usage isn’t extinct, but it is far less common than it used to be and IS largely extinct in casual day to day speech. We would say flee, run away, escape, or any of a dozen other things more often than “flight”