Drain pickles, reserving brine (about 4 cups). Place pickles in an airtight container. Store, covered, in the refrigerator up to 2 weeks. Add chicken to brine in a large pickle jar or place in a large resealable plastic bag set in a bowl; seal jar or bag. Chill for 8 to 24 hours.
Preheat oven to 475 degrees F. Remove chicken from brine; pat dry. 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 degrees 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.