My opponent is playing U/W fish and has an Aether Vial in play with 2 counters. It is the beginning of my upkeep. I have two Dark Confidants in play.
The first card I reveal is Chain of Vapor. My opponent then activates his Vial putting Meddling Mage into play naming Chain. I argue that I put Chain of Vapor in my hand and therefore can cast it in response to his vial activation on a target already in play. He says he can act between the revealing and putting of the card into my hand. Am I correct? Would not my foe have to have used vial before the Confidant trigger ever resolved and therefore before he even knew that Chain of Vapor was going to be revealed?
Correct. Players can only play abilities or spells when they have priority, and players don't have priority while another ability/spell is resolving. And, as you say, while Vial's ability is on the stack, you can then play Chain of Vapor.
Related topic: Can I say resolve the 1st Confidant revealing, say, Vampiric Tutor and then use Vampiric Tutor before the 2nd Confidant triggers?
Not before it triggers, since players don't gain priority to play spells or abilities until after all beginning of upkeep triggers have been checked and placed on the stack. Replace 'triggers' with 'resolves', and the statement would be correct.
Side note: I should know this but if I have an effect that lets me sacrifice mana crypt during my upkeep, e.g. Smokestack or Energy Flux, I still have to flip correct?
Correct (barring cards like Stifle, of course).