Step 1Combine the pepper flakes, cinnamon, coriander and salt in a small dish. Sprinkle half the mix on top of the duck breasts, dividing evenly. Gently pat the seasoning in place with your hands.
Step 2Heat the oil and butter in a large nonstick skillet over medium-high heat. When hot, place the breasts, seasoned side down, in the skillet. Sprinkle the remaining seasoning over the unseasoned side of the breasts. Cook, uncovered, turning only once, until the underside is browned, about 3 minutes total for rare, about 5 minutes total for medium. (The meat becomes tough when well done.)
Step 3Transfer the duck to a warm platter. Cover with foil; let rest 5 minutes.
Step 4To serve, cut each breast across the grain on a slight angle. Place each on the cooked spaghetti squash, fanning out the slices. Drizzle with any pan juices. Top the duck breasts with about 2 tablespoons of Warm Cranberry Apple Chutney. Serve hot, passing any remaining warm chutney separately.