Heat 1 tablespoon butter in a large skillet over medium-high heat. Cook the sausage until golden, about 2 minutes. Season the chicken with salt and pepper, then toss with the flour in a bowl; add to the skillet and cook until browned but not cooked through, about 3 minutes.
Add the onion, peppers, garlic, 1/2 teaspoon salt, and pepper to taste and cook 3 minutes. Add the wine, scraping up any browned bits; bring to a boil and cook until slightly reduced, about 1 minute. Add the broth and bring to a gentle simmer. Cover and cook until the sausage and chicken are cooked through, about 5 minutes.
Transfer the chicken, sausage and vegetables to a platter with a slotted spoon. Increase the heat to high and stir the parsley and cherry peppers and their liquid into the skillet; boil until reduced by one-third, 2 to 3 minutes. Remove from the heat and stir in the remaining 1 tablespoon butter. Pour the sauce over the chicken mixture.