Combine brine ingredients in a large stock pot and add the chicken. Place in refrigerator for 2 hours.
Preheat oven to 400 degrees F. Place a wire rack over a baking sheet.
Mix flour with dry Italian dressing and place into a shallow dish.
Remove drumsticks from brine and rinse then dry with paper towels. Brush each drumstick with olive oil and coat in flour mixture. Place drumsticks, on wire rack so that they are evenly spaced and not touching each other.
Bake in preheated oven for 30 minutes. Turn all drumsticks over and bake another 30 minutes. Juices should run clear.