does vigilant strike work with cast on damage taken?

?

No.

There is no interaction between Vigilant Strike and CWDT.

Skills in this game can be Attacks, Spells, or neither. CWDT can only trigger Spells. Vigilant is an Attack, which you can see by mousing over it and reading "Attack" in its list of gem tags under the gem name. When something is am Attack you know that it is not a Spell.

The way to achieve what you are trying to do would have been to use Fortify Support + Vengeance, but there is a hidden rule that triggered skills cannot grant Fortify.

IMO that's bad tooltip design. They need to add "Cannot be granted by Triggered Attacks" to the Fortify gem.