Just a quick clarification as I want to be sure.

In my example it's turn 2, I have two face down-plot twists (Made Men and Honor Among Thieves) and only a one drop in formation (Vulture). Is it legal to exhaust Vulture, flip Made Men to give him Crime Lords and then flip Honor Among Thieves, thus teaming the two affiliations?

Yup. He's both affiliations for the turn, so Honor is a legal play.

Thank you! :)

For reference, you would actually be flipping up Made Men, then exhausting Vulture to play the effect. You can't pay for Made Men's effect before you've flipped Made Men up.