In a bowl, whisk together the vinegar, honey, soy, brown sugar, garlic, and red pepper flakes. Marinade the drumsticks in the mixture in a shallow covered dish or a sealed plastic zipper bag in the refrigerator for at least 2 hours, up to 24.
Preheat the oven to 450 degrees. Line a baking sheet with aluminum foil. Set a cooling rack on top of the baking sheet. Remove the chicken from the marinade and place the drumsticks onto the cooking rack. Transfer the marinade to a small saucepan. Set aside. Roast the drumsticks in the preheated oven for 30 minutes.
Meanwhile, simmer the marinade on the stove over medium-low heat until reduced and thickened, about 15 minutes.
Remove chicken from the oven, brush generously with the reduced marinade, and return the chicken to the oven for another 10 minutes. When the chicken is done, sprinkle with sesame seeds and sliced green onions and serve.