Place flour in a shallow dish. Sprinkle chicken with salt and pepper. Dredge the chicken in the flour (reserve excess flour). Heat 3 teaspoons oil in a large skillet over medium-high heat. Cook the chicken until golden on the first side, 2 to 4 minutes. Reduce heat to medium, turn the chicken and cook until the other side is golden, 2 to 4 minutes more. Transfer to a plate.
Add the remaining 2 teaspoons oil to the pan and heat over medium heat. Add shallots and cook, stirring, until just starting to brown, 2 to 3 minutes. Add grapes and cook, stirring occasionally, until just starting to brown, 2 to 3 minutes. Sprinkle with 5 teaspoons of the reserved flour; stir to coat. Add wine and broth; bring to a boil, stirring constantly. Reduce heat to a simmer and cook, stirring occasionally and scraping up any browned bits, until the sauce is reduced and thickened, about 8 minutes. Stir in parsley.
Return the chicken to the pan, turning to coat with sauce, and cook until heated through, about 2 minutes. Serve the chicken with the sauce on top.
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