1. Preheat oven to 350°F. Trim excess fat from chicken and season on all sides with salt and pepper. Melt butter with oil in a large skillet over medium-high heat. Place flour in a bowl; add chicken, turning to coat. Shake off excess and place chicken, skin side down, in skillet. Discard leftover flour. Cook chicken until golden brown, about 7 minutes. (If skillet is too small, cook in batches.) Transfer to a large baking dish, skin side up. Bake until meat near bone shows no traces of pink, about 25 minutes.
2. Pour off fat from skillet and return skillet to medium-high heat. Add wine and cook, stirring to pick up any browned bits on bottom, until liquid is reduced by half, about 2 minutes. Add broth, increase heat to high and boil rapidly until reduced and thickened, about 2 minutes. Reduce heat to medium-high; stir in preserves. Cook, stirring often, until thickened and glossy, about 5 minutes. Stir in cherries and cook until warmed through, about 3 minutes. Season with salt and pepper.
3. Arrange chicken on plates or a platter. Spoon cherry sauce on top and serve warm.