Hard to give a definitive answer because persuading a captured unit relies on luck. I definitely think you can persuade the Flier before endgame but to decrease the chances of getting rng screwed you'll probably need to save 1-2 paralogues and/or invasions until after Chapter 24. If I tried this out, I would probably save Invasion 2 and 1 of the easier paralogues because some of them get insanely hard during the late game chapters (Siegbert, Shiro, etc). My choice would be either Dwyer or Shigure because you can pretty much just kill the boss turn 1 and get the next persuade attempt going. Not sure if you're currently in the middle of a playthrough or just starting a run, but a more reliable method for a Flier with pass would be to use the Azura/Niles pairing and let Shigure inherit Pass from Adventurer Niles. Both children gain decent offensive stats (Nina moreso due to her magic and the blessed bow) but you'll most likely be using Shigure as a staff/rallybot.

or maybe im sped i didn't do calculations so lmk if im wrong