Place vinegars and sugar in a medium nonreactive saucepan and cook over medium-high heat until the sugar is completely melted and the mixture is reduced by 1/2 and is thick. Carefully transfer the mixture to a blender. Add the chili and mint and blend until smooth. Season with salt. Let the glaze cool to room temperature.
For the jerk rubbed chicken:
Combine the spices and salt in a medium bowl. Preheat griddle to medium or heat griddle pan over medium heat. Rub 1 side of each chicken with 2 tablespoons of the jerk rub and drizzle with canola oil. Griddle, rub-side down for 3 to 4 minutes or until a crust has formed. Brush with some of the chili-mint glaze and turn the chicken over and continue griddling for 7 to 8 minutes or until just cooked through. Brush with more of the glaze and serve immediately.