Stir the salt and pepper into the flour until mixed. Toss the chicken in the flour mixture.
Put the olive oil and butter in medium sauté pan and heat it over medium heat until the butter is melting and slightly sizzling (“singing”). Add the chicken thighs skin side down and cook for 3-4 minutes until the skin is browned and the chicken pieces easily release from the pan. Turn the thighs and repeat on the other side. Do this in batches if needed.
Once the chicken is browned, put it in an oven-proof pan and place it in the preheated oven to finish cooking for 30-40 minutes while you make the sauce.
Pour all but a thin film of oil from the pan and return it to medium-low heat. Add the diced onion and cook, stirring occasionally until it is softened and opaque.
Add ½ cup of blueberries, the vinegar, honey and rosemary to the onions in the pan and bring to a low boil, stirring and scraping the bottom of the pan to release the browned chicken bits. Let it simmer for 2-3 minutes until slightly thickened.
Taste and add salt if needed. Just before serving stir in ¼ cup fresh blueberries
Serve the chicken over rice and top with the sauce.