Heat the oil in a skillet over medium heat. Place turkey in the skillet, and cook until evenly brown; drain.
Coat the inside of a slow cooker with cooking spray, and mix in turkey, tomato soup, kidney beans, black beans and onion. Season with chili powder, red pepper flakes, garlic powder, cumin, black pepper, allspice and salt.
Cover, and cook 8 hours on Low or 4 hours on High.