There is very little information given about Kidd himself, probably because he is not directly relevant to the story, and to preserve a sense of mystery about him, which adds to the legendary and foreboding aura that surrounds his buried treasure.
Indirect characterization consists of what we may infer about a character's nature based on their words, actions, and so forth, as opposed to things that we are directly told by the narrator; by comparison, Tom and his wife are directly characterized as misers, whereas nothing is said about Kidd other than his having been "hanged for a pirate", which might suggest that he wasn't or that the legal justification for his hanging was flimsy.
One subtle point of characterization is that the inlet where the treasure is buried is said to provide a good place for a boat to land at night, and keep a lookout. This implies a suspicious and secretive nature about Kidd. It is also said that the Devil took the treasure under his guardianship, but this was customary for stolen things being buried, and so it might imply that Kidd had a more familiar as well as businesslike interaction with the Devil, perhaps on multiple occasions.