Rinse the chicken and pat dry; sprinkle with 1 teaspoon salt, then toss with the flour. Heat the olive oil in a Dutch oven or deep skillet over medium-high heat. Add the chicken, skin-side down; cover and cook until browned, 5 to 6 minutes per side. Transfer to a plate and set aside.
Add the onion, rosemary and red pepper flakes to the pot and cook, stirring occasionally, until the onion starts to brown, about4 minutes. Add the wine, scraping up any browned bits from the bottom of the pot. Stir in the tomatoes and 1/2 cup water.
Return the chicken to the pot, skin-side up. Cover and bring to a rapid simmer. Uncover, spoon the sauce over the chicken and continue simmering until cooked through, about 8 more minutes.
Meanwhile, cook the polenta as the label directs; season with salt and pepper. Serve with the chicken.