Combine flour, poultry seasoning, 1 teaspoon of the thyme, salt and pepper in a large resealable bag; add chicken pieces to bag and toss to coat.
Heat 1 tablespoon oil in a large nonstick skillet over medium-high heat. Remove chicken from bag with a slotted spoon, shaking off excess flour. Set remaining flour mixture aside and add chicken to skillet. Cook for 5 minutes, stirring occasionally, or until browned; place in slow cooker.
Add remaining 1 tablespoon oil to skillet and stir in carrots, celery, potatoes, mushrooms and onion; cook, stirring often, for 5 minutes. Stir remaining flour mixture into skillet and cook 1 minute. Add broth to skillet and bring to a boil. Pour skillet contents into slow-cooker bowl. Cover and cook on HIGH for 4 hours or LOW for 7 hours.
When there is 1 hour cook time remaining, stir together biscuit mix, milk and remaining 3/4 teaspoon thyme. Drop biscuit mix by the tablespoonful over top of chicken mixture. Cover slow-cooker bowl with a cotton dish towel and place lid over top. Continue cooking until biscuits are cooked through.