He was the one who recommended Torres for chief engineer. This doesn't speak well for his true loyalty to Voyager. More likely, it suggests he wanted to get the ship destroyed before they get back home. He frequently objected to Janeway's decisions, but he would turn around and tell his former Maquis crew to obey her orders anyway since she's the captain.
Chakotay and Janeway's relationship seems to sway back and forth from teetering on romance to counter point. I guess her genocidal rampages were just too much for him. However, by the end of the series, Chakotay hooks up with Seven of Nine for no particular reason.
Chakotay embodies just about every Hollywood stereotype concerning American Indians there is. He is supposed to be Mayan, yet he pursues vision quests and believes in animal spirit guides. People use a medicine wheel and coyote stones  to try and heal him. He insists on not even scanning a burial site to avoid violating its "sanctity". Hawks are sacred symbols of his people and messengers of the spirits, etc. Just as Neelix takes every opportunity to tell stupid personal anecdotes, Chakotay is always ready with one of the "sacred legends of his people". And to make it all even worse, this was apparently all programmed into American Indian genetics by alien visitors thousands of years ago.
If Voyager had gone on longer, its entirely possible the writers would have had him open a casino next to Neelix's galley.