Preheat the oven to the lowest temperature.
Cut the chicken breasts in half horizontally, butterflying them open (if the pieces are large, cut them each into 2 pieces after you cut them in half). Put chicken pieces between 2 pieces of parchment paper and pound them with a heavy skillet until ¼-inch thick.
Mix together the flour, salt, and gluten-free spice blend. Rinse the chicken pieces in water, then dredge thoroughly in the flour mixture until well coated. Heat the olive oil and 2 tablespoons of the grapeseed oil in a large skillet over medium-high heat. Add half of the chicken pieces and brown well on each side, about 3 minutes per side.
Transfer to an ovenproof plate, add the other breasts and cook, then remove from the skillet. Place the chicken breasts in the oven to keep warm while preparing the sauce. Add lemon juice, chicken stock, and capers to the skillet and use a metal spatula to loosen the browned bits and incorporate them into the sauce.
Reduce the sauce by ½, then whisk in the remaining grapeseed oil. Plate the chicken, pour the sauce over it, and garnish with the parsley. Serve.