Line 2 baking sheets with aluminum foil; grease the foil with cooking spray.
Place the chicken in a large mixing bowl. Season with salt, pepper, and hot sauce. Add the olive oil; toss to coat.
Place the flour and wings in a large, food-safe plastic bag. Hold the bag closed tightly, and shake to coat the wings entirely with the flour; no wet spots should remain.
Arrange the wings on the prepared baking sheets, making sure none of the pieces are touching one another. Spray wings with additional cooking spray
Bake in the preheated oven for 30 minutes, turn all the wings, and return to the oven to cook until crispy and no longer pink in the center, about 30 minutes more.
Whisk together the garlic, ginger, chili sauce, balsamic, brown sugar, and soy sauce in a saucepan. Bring the mixture to a boil and immediately remove from heat.
Put about half the wings in a large mixing bowl. Pour about half the sauce over the wings. Toss the wings with tongs to coat evenly; transfer to a tray and allow to sit about 5 minutes to allow the sauce to soak into the wings before serving.