Preheat a large skillet with 2 tablespoons of oil. Over high heat, brown chicken breast cubes until lightly lightly golden brown. Remove the chicken and set aside. You may want to do this step in two or three batches, adding one tablespoon of oil each batch.
Add one more tablespoon of oil to the skillet. Cook chopped onions and garlic, constantly stirring, until golden brown. Remove the onions and set aside.
Add another tablespoon of oil to the skillet and cook sliced carrots and celery over high heat, constantly stirring, for about 2 minutes.
Toss chicken breasts, carrots, celery, onion, garlic, sweet peppers, and potatoes into the slow cooker. Add 3 tablespoons all-purpose flour to hot chicken stock and stir well to disperse the flour in the chicken stock. Pour the chicken stock into the pot. Cook on the lowest setting for about 6 hours. Add 1 teaspoon kosher salt, 1/2 teaspoon ground black pepper, one tablespoon of chopped scallions and one tablespoon of chopped dill 20 minutes before the stew is done and stir. Taste and add more salt if necessary.
Garnish with the remaining chopped scallions and dill and serve.