Preheat the oven to 425°F.
Place the flatbreads on a parchment-lined baking sheet.
For a crispier crust, pre-bake the flatbreads for 3 minutes.
Toss the cooked chicken with 2 tablespoons barbecue sauce.
Spread the remaining barbecue sauce evenly over the flatbreads, leaving a small border around the edges.
Sprinkle half of the mozzarella over the sauce.
Add the barbecue chicken and red onion.
Top with the remaining mozzarella and cheddar if using.
Bake for 8–12 minutes, or until the cheese is melted and the edges are crisp.
Rest for 2 minutes, then garnish with cilantro, green onions, or red pepper flakes if desired. Slice and serve warm.