Pat chicken thighs dry and season thoroughly with Cajun seasoning, paprika, and black pepper.
Dredge seasoned chicken in flour, shaking off any excess.
In a large heavy-bottomed skillet or Dutch oven, heat vegetable oil over medium-high heat. Sear chicken skin-side down for 5-7 minutes until golden brown, then flip and sear for 3 minutes. Remove chicken and set aside.
In the same pan, sauté onion, bell pepper, and celery in the remaining fat until softened (approximately 5 minutes). Add garlic and cook for 1 minute until fragrant.
Whisk in both cans of condensed soup and the chicken broth, scraping the bottom of the pan to release browned bits (fond).
Stir in the uncooked rice until evenly distributed in the liquid mixture.
Nestle the seared chicken thighs back into the rice and liquid base.
Bring to a gentle boil, then reduce heat to low, cover tightly, and simmer for 30-35 minutes until the rice is tender and chicken reaches an internal temperature of 165°F.
Remove from heat and let stand, covered, for 5 minutes to allow the steam to finish the rice before serving.