Whisk together flour, 1/4 teaspoon salt, and 1/4 teaspoon pepper in a pie plate or shallow bowl. Pat chicken dry, then dredge legs, 1 at a time, in flour, shaking off excess. Transfer to a sheet of wax paper, arranging chicken in 1 layer.
Heat oil in a 12-inch heavy skillet over moderately high heat until hot but not smoking, then brown chicken, skin sides down first, turning over once, 6 to 8 minutes total. Transfer chicken to a plate, then pour off all but 1 tablespoon fat from skillet.
Add shallots to skillet and sauté, stirring occasionally, until golden brown, 2 to 3 minutes. Add wine and deglaze skillet by boiling, stirring and scraping up brown bits. Add broth, mustard, and remaining 1/4 teaspoon salt and pepper. Bring to a simmer, then return chicken to skillet, skin sides up, along with any juices from plate, and cook over moderate heat, covered, until chicken is cooked through, about 25 minutes. Transfer chicken to a platter and boil sauce until reduced to about 1 cup and slightly thickened, 3 to 5 minutes. Remove from heat and stir in dill, then pour sauce over chicken.
