Heat grill to medium. Combine all spice ingredients in a medium bowl.
Brush chicken on both sides with the oil and season with salt. Rub 1 side of each breast with some of the jerk seasoning. Place the chicken on the grill, rub side down and grill until slightly charred and the rub has formed a crust, about 5 minutes. Turn the chicken over, brush the top side with some of the Habanero-Mint Glaze and continue cooking until just cooked through, brushing with more of the glaze every few minutes. Remove from the grill to a serving platter, brush with more glaze and let rest 5 minutes. Serve with Mango Relish on the side.
Place vinegars and habanero in a medium nonreactive saucepan and bring to a boil over medium heat. Add the sugar and cook over medium-high heat, stirring occasionally, until the sugar is completely melted and the mixture has thickened and reduced by about half. *Carefully transfer the mixture to a blender, add the mint and blend until smooth. Season with salt and let the glaze cool to room temperature.
*When blending hot liquids: Remove liquid from the heat and allow to cool for at least 5 minutes. Transfer liquid to a blender or food processor and fill it no more than halfway. If using a blender, release one corner of the lid. This prevents the vacuum effect that creates heat explosions. Place a towel over the top of the machine, pulse a few times then process on high speed until smooth.
Combine all ingredients in a large bowl and season with salt and pepper, to taste. Let sit at room temperature for 30 minutes before serving to allow flavors to meld. May be prepared and refrigerated, covered, up to 1 day ahead. Bring to room temperature 1 hour before serving.