Preheat oven to 425 degrees F. Place a baking sheet on the center rack to preheat.
Season the chicken: toss shredded chicken with half the BBQ sauce, garlic powder, smoked paprika, salt, and pepper.
Prep the flatbreads: brush both sides of each flatbread lightly with olive oil.
Add toppings: spread remaining BBQ sauce over each flatbread. Top with mozzarella and optional Gouda, then BBQ chicken, then sliced red onion and jalapeños if using.
Bake: slide flatbreads onto the hot baking sheet. Bake 10 to 12 minutes until cheese is melted and bubbly and edges are golden.
Finish and slice: rest 2 minutes, drizzle with extra BBQ sauce, scatter cilantro, and slice. Serve with lime wedges if desired.