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Sprinkle the chicken thighs with salt and pepper, then toss them in a bowl with the flour to lightly coat.
Heat the olive oil in a large, wide pot over medium-high heat until shimmering. Add the thighs and cook, turning once, until golden brown on both sides, about 3 minutes per side. Remove the thighs to a plate.
Add the onion and mushrooms to the pot and cook, stirring, until the onion is softened and the mushrooms are lightly golden, about 5 minutes. Add the garlic and bell peppers and cook, stirring, until the peppers are just starting to soften, about 1 minute. Add the wine and bring to a boil, then cook, scraping up any brown bits, until reduced by about half. Add the oregano and rosemary. Add the tomatoes and their juice and bring to a simmer. Add the olives and capers. Return the chicken to the pot, nestling in the sauce. Reduce the heat to keep the sauce at a gentle simmer and cook until the chicken is cooked through, about 25 minutes.
Sprinkle with the basil. Serve immediately.