Heat olive oil in a skillet over medium heat, and brown the chicken breasts on both sides, about 5 minutes per side. Place the chicken breasts into a slow cooker. Cook the onion, red bell peppers, and garlic in the hot skillet until the onions are translucent, about 5 minutes; transfer the cooked vegetables into the slow cooker.
Stir the crushed tomatoes, sweet potatoes, carrots, chicken broth, curry powder, cumin, chili powder, cayenne pepper, red pepper flakes, cinnamon, and black pepper into the slow cooker. Set the cooker to High, and cook for 5 to 6 hours, or cook on Low for 10 hours. Stir in additional chicken broth throughout the cooking time if needed.
Mix in the brown rice 3 hours before serving, and mix in the peanut butter at least 1 hour before serving. Shred chicken meat, and serve hot.