If a person plays Double Slap on me, can I use the triple card combo to steal someone else's Nope card, then play that Nope card on the Double Slap to avoid drawing?
Nope. You can't do that.
The rules (under the section on Nope) specifically state that:
You can play a Nope Card at any time before an action has begun, even if it’s not your turn.
As soon as you begin your first turn as a result of the Double Slap then you are accepting that the Double Slap card is in effect.
The only way the Double Slap could be negated is if you, or another player, played a Nope card directly on it before you start your first turn that results from the Double Slap.