Drain pickles, reserving brine (about 4 cups). Place pickles in an air-tight container. Store, covered, in the refrigerator up to 2 weeks. Add the chicken to the brine in a container, jar or baggie; seal. Chill 8-24 hours.
Preheat oven to 475* F. Remove chicken from brine; pat dry with paper towels. Discard brine. In a small bowl combine flour and pepper. Coat chicken with flour mixture; shake off any excess.
In a large, heavy ovenproof skillet heat oil over medium-high heat. Add chicken, skin side down; sear until golden brown, about 8 minutes. Turn chicken; transfer skillet to oven. Bake 15 minutes or until juices run clear (180*F). Remove from oven. Transfer chicken to platter; let rest 5 minutes.
Return skillet to stove. Remove fat from skillet, reserving 1 Tbsp in the pan. Return skillet to heat. Add wine; bring to boiling over medium-high heat. Using a wooden spoon, scrape the browned bits from the bottom of the pan until wine nearly evaporates, about 2 minutes. Add broth; bring to boiling until reduced to about 1/2 cup, about 2 minutes. Stir in butter. Season to taste with pepper. Remove from heat; stir in dill. Pour sauce over chicken. Top with chopped pickles and red sweet peppers before serving.