Heat a large, cast-iron skillet over medium-high heat.
Season chicken with salt and pepper, and dredge in flour; shake off excess. Add 2 tablespoons of oil to the pan, 2 turns of the pan and brown half of the chicken until crispy and golden on both sides. Remove to a plate, add more oil as necessary and repeat with remaining chicken. Brown both lemon halves, cut-side-down, to caramelize the flesh; reserve.
Add the sausage to the drippings in the pan and brown and crumble; remove. Add peppers, onions, garlic and rosemary, and season with salt and pepper. Stir 5 minutes to soften then add wine and stir 1 minute. Add chicken stock and slide chicken and sausage back in. Simmer and thicken; stir in juice of caramelized lemon and swirl in the hot peppers and a splash of their juice.