Who is driving Thomas Jane's hair and wardrobe on the Expanse?

My guess is that Jane himself is driving his character's look, possibly as a fan of the artists I mentioned, facilitated by wardrobe and makeup people with an appreciation of that aesthetic.

As far as I'm aware, there is no proof of that.

However, there is a tiny bit of supporting evidence that Joe Miller (the character played by Jane) drives his own personal style.

Miller's partner What's the deal with the hat?
Miller Keeps the rain off my head.

(I can't recall Miller's partner's name at the moment)

Miller's response is bullshit, since there is no weather inside a space station. He chooses to wear the hat for personal style reasons, and only forgoes it when necessary (e.g. wearing a space suit).

If Miller wears the hat out of a personal sense of style, it stands to reason that he does the same for his hair and wardrobe, since they all seem to fit the same general aesthetic.
It also fits with Miller's personality. He doesn't care what people think of him, he simply does what he feels is the right thing to do. Miller's sense of style is questionable both in-universe and out-of-universe, but Miller does not feel any shyness about who he chooses to be.

Edit
As to Miller's style clashing with the general attire of the Belters; that can be done to justify how Miller doesn't belong. He is from somewhere else, and a contrarian at heart; so the show's creators (and the author of the book) can use this as a way of visualizing Miller not fitting in with the crowd.