Note: The vinaigrette can be made 1 week ahead. Cover and chill. Shake to reincorporate just before serving.
Season chicken wings with salt and black pepper. Transfer the wings to a large resealable plastic bag and add 1 cup vinaigrette. Seal bag and shake to coat. Chill for at least 2 hours and up to 1 day.
Prepare grill: Heat grill to medium heat. Grill chicken, turning occasionally, until wings are evenly charred and cooked through, 8 to 10 minutes if separated, 12 to 15 minutes if left whole. Transfer to a platter.
Meanwhile, toss shishito peppers and oil in a medium bowl; season with salt and black pepper. Grill, turning occasionally, until charred in spots and blistered, about 3 minutes. Transfer to platter with wings.
Scatter jalapeño over wings and shishito peppers. Drizzle with ¼ cup vinaigrette.