Place flank steak in a shallow dish; pour marinade over steak. Cover and chill at least 2 hours or up to 8 hours. Remove steak from marinade, and pour marinade into a small saucepan. Stir in brown sugar.
Bring marinade to a boil over medium-high heat. Reduce heat to medium, and simmer, stirring often, 3 to 4 minutes or until slightly thickened. Remove from heat.
Coat cold cooking grate with cooking spray, and place on grill over medium heat (300° to 350°). Place steak on cooking grate, and grill 10 minutes; turn and grill 8 more minutes or to desired degree of doneness. Serve with marinade.