Heat a dutch oven or big pot over medium-high heat; add oil to pan. Add sausage and cook 3-4 minutes or until browned. Add onion, celery, green bell pepper, and garlic; sauté 5-6 minutes or until tender.
Add rice, water, red pepper flakes, salt, thyme sprigs, chicken broth, diced tomatoes and bring to a boil. Stir, cover, reduce heat, and simmer 20-30 minutes or until rice is done. Remove from heat.
Remove thyme sprigs and discard. Add shredded chicken and fold in to combine. Let sit 5 minutes to allow chicken to heat through.
Recipe adapted from Cooking Light.