Considering neither of those cards are kinds of effects you can use Barrel on anyway, that wouldn't help.
The Immortal of Thunder doesn't inflict damage.
Barrel Behind the Door can only be chained to the ACTIVATION of a Spell/Trap Card (IE, when it's placed face-up on the field), not to the effect of one, hence why Aegis of Gaia doesn't work.
Destruction of Destiny isn't guaranteed to deal damage, so you can't use it on that, either. (Or other cards that aren't guaranteed to, like Time Wizard or Dicephoon.)
actually, BBtD should work even against the effect of an already face-up card, it just needs the effect to be an ACTIVATED one.
Some cards have ruling that says the part of their effect that inflicts damage to you is not considered an activated effect (and therefore does not start a Chain). These cards' damage cannot be chained with BBtD.
Anoymous
^x4
