Mix flour, basil, thyme, sage, and black pepper in a large resealable bag; add chicken, seal bag, and shake until chicken is evenly coated.
Heat olive oil in a large skillet over medium heat; cook and stir onion and bell pepper until slightly tender, 5 to 10 minutes. Add chorizo sausage and garlic; cook and stir until sausage is cooked, about 5 minutes. Transfer mixture to a slow cooker and top with mushrooms.
Cook and stir coated chicken (including all the flour) in the same skillet, adding more oil if needed, until chicken is browned, 5 to 10 minutes. Transfer chicken to the slow cooker.
Pour chicken stock into the same skillet, and bring to a boil while scraping the browned bits of food off of the bottom of the skillet with a wooden spoon. Pour all the liquid and brown bits into slow cooker.
Mix cream of mushroom soup, cream of celery soup, sour cream, Cajun seasoning, and cayenne pepper in a bowl; spoon into slow cooker.
Cook on High for 2 hours; reduce setting to Low and cook for 4 more hours.