Nearly 600 hit points, and regen into the bargain... I trust people won't be complaining about this one being too fragile.
Her legendary actions are interesting. Moloch and the sibriex relied very heavily on LAs for out-of-turn shenanigans; the sibriex especially needs its LAs for action denial, otherwise it gets pounded into paste in the first round. Zariel only has two LAs: A 120-foot teleport, and an extremely weak attack that costs two LAs for a quarter her regular Multiattack damage.
Since Immolating Gaze is so weak, Zariel is probably best served by relying heavily on teleportation, with IG as a fallback if she can't think of anything creative. With her fly speed and teleport, she can cover 510 feet per round, which allows her to do bombing runs with javelins or fireballs and get out of range of most retaliation (an archer could still hit her but would be rolling at disadvantage). She could also teleport next to an archer or caster, forcing that PC to either attack with disadvantage or eat a godawful opportunity attack for breaking contact. And if she's getting low on hit points, she can teleport, move, and Dash to flee at 660 feet per round. Break contact, hide for a few minutes, and regenerate back to full, then renew the assault.
As archdevils go, Zariel seems pretty straightforward. She's a big, tough, flying beater. The Horrid Touch is a vicious debuff (would be nice to know if there's supposed to be an initial save, or if you're automatically blind/deaf for 1 round before your first saving throw; also, what kind of saving throw is it?), but other than that, she doesn't have a lot of tricks up her sleeve. Just a steady torrent of damage, round after round.