In a large dutch oven on a cooktop set to medium high heat, add oil and flour and stir until lightly toasted. Flour should be light brown. Lower temperature to low and add sausage, ham, onion, green pepper, garlic, green onion and parsley. Cook and stir to combine well with flour mixture (about 10 minutes). Add 1/2 cup of the strained chicken stock and stir until combined.
Add shredded chicken, salt, pepper, thyme, cayenne and bay leaves. Mix to combine and then add remaining chicken stock. Raise heat until the mixture boils and then lower to simmer. Cook uncovered, stirring occasionally for 1 hour.
Remove pot from heat, add filé powder and stir until combined well. Let sit for 5 minutes and serve hot over rice.