Do Arcane Aegis and Arcane Barrier stack?

[Dhaaaan]

Like for some ultimate shield gating? How do they interact together?

[Robert Zerker]

Aegis triggers when damage is done to shields : it gives a 30% bonus (adding to your innate frame shield regen, which starts as the arcane is triggered) of shield regeneration lasting 12s, even under enemy fire.

Barrier also triggers when damage is done to shields, but here it's a chance to get back to full shield capacity.

They don't interact together at all properly speaking, but their effects can stack.

Considering Shield Gating, it could -in theory- shorten the time your 'gating' is unavailable IF you have already regen a bit of shields back, to be damaged in the first place, to then trigger the arcanes.
So, it's not that good for that purpose if you have the dragon key and low max shields, since you will probably not survive the hit which was supposed to trigger the arcanes, at high level.
It's only ok-ish on frame with huge shield capacity + adaptation. Or Hildryn.