The entire point of this movie is that it is a reversal of common action movie tropes.
Throughout the movie, Jack, who is supposedly the hero (and who certainly thinks he is), is consistently upstaged by Wang, ostensibly the "sidekick". He is pulled along by the momentum of the story, never really understanding what's going on, never truly in control, and so he bumbles his way through fights and is just generally a step behind everyone else.
Apart from his Crowning Moment of Awesome against Lo-Pan ("it's all in the reflexes"), he never really accomplishes anything in the movie without someone else's help. It's actually an acceptance of this that allows this moment to happen. After missing the first throw and realizing that he's pretty much screwed everything up, Jack stops trying to be the star and decides to let things play out as they must. He looks at his fate, shrugs, and says, "What the hell."
The last scene is also a reversal. Jack offers to give up the open road for Gracie, where in most westerns, it's usually the woman who tries to tame the wild cowboy drifter and stop his wandering. Gracie turns down the offer and counters that she could come with him, which Jack finds tempting, but in the end, he refuses as well because he knows that these sorts of 'happily ever after' stories probably don't work in the long run.
He also knows he's not relationship material, and he cares for Gracie too much to subject her to that. He prefers to hurt her a little now instead of hurting her a lot later. Refusing the last kiss is part of that. It's a promise that he doesn't want to make to her, right up to the "See you round"/"Never can tell" exchange.