Nothing would happen with Armour of Agathys, since it specifies a "Melee" attack. While Warding Bond is considered a Spell.
But something like say, Cindermoth Cloak will trigger and yes, you can set your bonded target on fire, dealing damage, which goes back to the caster... Which triggers Cindermoth Cloak...
It's a pretty odd interaction to say the least.
Well, that's already an inconsistency. If it changes the attack from melee to magic, but keeps the damage type for resistance... Because one can have resistance to normal damage and not to magical damage. It looks kinda messy. For a human DM this seems quite horrible to track.
I guess that, if I was a 5E DM, I'd just make the houserule that it transfers the damage from the victim to the protector, as it is. That's also what it says literally in the BG3 description.
