Season the chicken with 1 tsp. salt and 1/2 tsp. black pepper. Spread the flour on a plate, and lightly dredge the chicken in the flour. Heat 2 Tbs. of the oil in a large Dutch oven or casserole over medium-high heat until the oil is shimmering hot. Cook the chicken in two to three batches (to avoid crowding the pot) until well browned on both sides, 2 to 3 minutes per side. Transfer each batch to a plate as it finishes, and if the pot looks dry between batches, add the remaining 1 Tbs. oil.
Return the chicken to the pot, add the green beans, garlic, 1/2 tsp. salt, and 1/2 tsp. black pepper, and cook, stirring, for 2 minutes. Add the red wine and cook until it almost completely evaporates, 1 to 2 minutes. Add the tomatoes and their juices, rosemary, and red pepper flakes. Bring to a boil, then lower the heat to a steady simmer. Cover, leaving the lid slightly ajar, and cook, stirring occasionally for 15 minutes. Add the olives, and continue simmering with the lid ajar until the chicken and green beans are very tender, about 5 minutes more. Season with salt and pepper to taste. Serve immediately.
The dish is complete as is, but nice with a crusty bread, or keep it Italian and serve Garlic-Parmesan Bread.