In a small bowl, combine salt, black pepper, chili powder, cumin, smoked paprika, and oregano to make the seasoning mix.
Heat olive oil in a large skillet over medium heat. Add the chicken pieces and sprinkle with the seasoning mix. Cook until chicken is browned and cooked through, about 5-7 minutes.
Add the chopped onion, minced garlic, and red bell pepper to the skillet with the chicken. Cook until the vegetables are softened, about 3-4 minutes.
Stir in the refried beans and water to the skillet, mixing well with the chicken and vegetables. Cook until everything is heated through, about 2-3 minutes.
Warm the flour tortillas according to package instructions to make them pliable.
Assemble the burritos: Lay a tortilla flat and spoon some Mexican rice down the center. Add a portion of the chicken and bean mixture, followed by corn and shredded cheese.
Fold in the sides of the tortilla and roll it up tightly to enclose the filling. Repeat with the remaining tortillas.
Serve the burritos warm with salsa and sour cream on the side.