In the dry skillet, toast the chiles on each side. Lightly toast the guajillo chiles and toast well the chiles de arbol (with the seeds).
Put all the chiles, garlic, cumin seeds, cloves, oregano, water, and cider vinegar into the blender. Blend at low speed until smooth.
With the meat mallet, pound each chicken breast until about ¾-inch (2 cm) thick. Rub the breasts with salt and put into the bag. Pour the adobo marinade over the chicken, seal, and turn the bag a few times to make sure the chicken is evenly coated. Let stand at room temperature for 1 hour or refrigerate for up to 1 day.
Heat a gas grill to medium-high or prepare a hot charcoal fire.
Grill the chicken for about 10-12 minutes, until it is cooked through and charred in places. Remove to a platter, cover with foil, and allow to stand about 5 minutes before serving.