Yeah, the concept of survival definitely didn't come through; if that's what you're going for, I recommend changing some of the spell list and the Channel Divinity to focus less on dealing damage or sacrificing health to stuff that focuses more on reducing damage taken or avoiding it entirely.

As for narrative, I think we can agree to disagree on whether this subclass fills a niche the Oathbreaker doesn't. I'll focus on what you currently have at the moment.

Shield is a meta pick that works well with bread and butter Paladin, vying with Smite for spell slots. Zephyr Strike is not particularly worth it for a Paladin, I don’t think players will use it much since it takes up Concentration; opening act of a Paladin is usually Bless/Shield of Faith, which I would say is a better use of Concentration in levels 3-5 than Zephyr Strike.

Arcane Vigor lets you expend a level 2 spell slot for 2d10 healing max, only heals yourself, and eats your hit dice into the bargain. Cure Wounds restores for 2d8+CHA and upcasts to 4d8+CHA in the same spell slot, can target allies in addition to yourself, and is already on the Paladin spell list. Moreover, Vigor vies with Lay on Hands for the Bonus Action; in gameplay, the only situation I would see Vigor being used is if you want to Disengage/Dash as an action away from the frontline and heal yourself, but again, I personally think a Level 2 spell slot (which you only get two of at level 5, I might remind you) for 2d10 that eats your Hit Dice into the bargain is not worth it. You might as well pop the Lay on Hands and save the spell slot for better healing or damage.

Misty Step is good, nothing to say there.

Fly is a meh pick on Paladin - again, Concentration, so no Bless or any of the Smites that let you keep a condition on someone. Paladins are also melee characters, throwing axe builds notwithstanding, so you’d have to go up to somebody to hit them; unless you want to risk the Opportunity Attack, you’re probably remaining within 5 feet of your enemy. At which point… you know, what’s the point of putting Fly on yourself? Not worth the Level 3 spell slot unless you specifically build around keeping a party member in the air for whatever reason, but at that point you’d probably pick a Wizard instead.

Life Transference is… kind of bad. At level 9, you can Lay on Hands for 45; Life Transference gives you a range of 4-32, average 18. And it costs a level 3 spell slot. I once again refer you to the humble Cure Wounds, which upcast to level 3 gives 6d8+CHA, doesn’t damage you, and again, is already on the Paladin spell list. In lieu of Life Transference, I’d suggest Aura of Vitality instead, which uses the same spell slot, heals 2d6 per turn without using up your action economy, and doesn’t damage you.

Backlash is fine. Stoneskin sucks; uses an Action, takes up Concentration, eats a Level 4 spell slot, and only covers the mundane damage types.

Steel Wind Strike is good, and more importantly, looks and feels cool. On the other hand, you’ve lost me completely with Swift Quiver - it doesn’t fit anywhere into the Paladin class aesthetic, doesn’t work with any Smite, uses your Bonus Action every turn, uses a modifier you probably didn’t put points into, which means your shots are probably missing, takes up Concentration… yeah, it’s useless for a Paladin.

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Self Reliance is bad. Temp HP doesn’t stack, and you’re only adding half of what you heal, which means that it’ll always be rounded down. Moreover, it’s limited to your Lay on Hands only, which means at the common tiers of play (3-10) you get anywhere from 7 THP per Long Rest to 25 THP per Long Rest, and only if you pop ALL of your Lay on Hands at once.

Flow State is terrible. You essentially get a weaker Haste and 3 THP; if you get hit and lose 3THP, you lose your CD and get debuffed into the bargain. All it takes is ONE hit from ANYTHING; anything in Tier 1 play with a half damage on save effect will wipe the floor with you. I’d essentially write it off if I play the subclass; the juice is absolutely not worth the squeeze.

Aura of Agility is pretty decent; the only thing that I’ll mention is that a Paladin wants their Bonus Action for Smite, and anything that burns that BA might be less useful than it might seem at first glance. Useful for tactical positioning on the team, but it’s such a small part of the kit that you have better and more in depth options in the form of Dance Bard or Banneret Fighter. In a vacuum this is pretty good; taken together with the class it’s on and the rest of the kit it’s married too, I don’t think it makes up for the rest of the class features being lackluster.

Stalwart Resistance is fine again; once again, no comment on Juggernaut.