Well I don't think Gui would openly admit to having any interest in someone just yet (though I may have him blush when he sees Jun again.) Maybe they got into an argument at an inn or tavern, leading to a drunken fight that got them both kicked out? I wouldn't mind having a sparing match between them near the beginning to settle any scores :P. Or if you prefer, maybe they fought alongside each other during a fire bender bandit raid on a town they both happened to be in by chance. 

Any ideas? I don't really have a preference myself.

EDIT: Also, just as a heads up, I edited Gaizen's "Other" section a bit.