The Hierophant signifies (formal) knowledge, and the power that comes from knowledge/study -- in some of the oldest decks, he's called the Pope. (As such, he's tied to the High Priestess -- there are a lot of cards in the Majors that represent "masculine" and "feminine" aspects of similar ideas.) Formal knowledge in Baccano! seems to me to be most clearly expressed in alchemy, and Huey is the one who seems most likely to use that for hierarchical power. Also, in the Thoth deck -- probably because of Crowley's attitude toward the church -- the Hierophant is always sort of a sinister figure; Crowley says that "He seems to be enjoying a very secret joke at somebody's expense." SO.
The Chariot is the card of triumph, of victory -- the image on the card is the warrior returning from battle, armored and crowned. In the Thoth deck, though not the Rider-Waite, he's carrying the Grail. I think it's probably pretty easy to see why Claire gets that one. ^^