In a medium saucepan, boil the vinegar over high heat until reduced by half, about 7 minutes. Add the blackberries and cook, stirring very gently, until they are just softened, about 2 minutes. Using a slotted spoon, transfer the blackberries to a bowl. Boil the liquid over high heat until reduced to 1/3 cup, about 3 minutes. Carefully pour the accumulated juices from the blackberries into the saucepan and boil for about 30 seconds longer. Season the reduction with salt and pepper and pour it over the softened blackberries.

Light a grill or preheat a grill pan. Using a sharp knife, score the duck skin in a crosshatch pattern. In a small bowl, mix the ancho powder with the coriander, cumin, and mustard powder. Season the duck breasts with salt and pepper and rub the spice mixture into the skin. Grill the duck breasts skin side down over moderate heat until lightly charred and crisp, about 3 minutes. Turn the breasts and cook for about 4 minutes longer for medium-rare meat. Transfer the duck to a carving board and let rest for 5 minutes.

Thinly slice the duck breasts on the diagonal and transfer to plates. Serve the duck with the blackberry sauce.

The blackberry sauce can be refrigerated overnight; reheat gently before serving. The spice-rubbed duck breasts can be refrigerated overnight; bring to room temperature before grilling.