For example: Would Zealot's Oath work with flasks or is it a seperate regeneration type?
Zealot's Oath will not cause Energy Shield to regenerate when using Life Flasks. Flasks recover life rather than regenerating it. Regeneration and Recovery are treated entirely separately despite having similar effects
As a nail in the coffin here's a quote from Mark_GGG, one of the developers:
The flask "recovery" is not quiet the same as life regeneration. I just tested it.
The flask will increase your life-regeneration for X seconds:
However... this will not work with Zealot. Zealot will NOT work with flasks and restore your energy shield, even if your ES-Recovery is triggered. I just tested this too. Your flask will heal your life and not your ES. Even if you trigger a flask during your normal ES-regeneration this will have effect at all to your ES-regeneration/s. The flask still regenerates your life.
Your normal life regeneration will be converted to a constant ES regen with Zealot: