HEAT oil in a small skillet over medium heat. Add flour and cook, stirring occasionally until fragrant and dark golden-brown, about 8 to 12 minutes.
MIX flour mixture, broth, okra, sausage, onion, bell pepper, celery, garlic and cayenne in a 4-quart slow cooker until combined.
COVER and cook on high for 4 hours, or on low for 6 hours, until fully cooked.
STIR in shrimp 1 hour before cooking finishes.
SERVE with rice.