Put the flour in a large shallow dish and season with the salt and pepper. Pat the chicken scaloppini dry with paper towels, then put them in the flour, coating the chicken on both sides. Set aside.
Heat the olive oil in a 14-inch cast-iron skillet over medium-high heat. Add the floured chicken and cook, in batches if needed, until deeply golden, about 3 minutes per side. Remove to a wire rack-lined sheet tray.
Reduce the heat under the same cast-iron skillet and add the onion, garlic and rosemary. Stir occasionally and cook until the onions are translucent, 3 to 5 minutes. Add the butter and capers and scrape the skillet as the butter melts to deglaze. Add the chicken stock and lemon juice, stirring to combine. Add the chicken pieces back to warm through and allow the sauce to reduce, another 2 to 3 minutes, spooning the sauce over the chicken to coat.
Garnish with the lemon supremes and serve.
To cut supremes, cut away the lemon peel and pith with a sharp knife to expose the lemon flesh, then cut the segments free of the membranes.