Season the turkey: Brush the turkey breasts with olive oil and season with smoked paprika, garlic powder, salt, and black pepper until evenly coated.
BBQ the turkey: Preheat the BBQ to medium-high heat. Grill the turkey breasts for 5–7 minutes per side, or until the thickest part reaches an internal temperature of 165°F (74°C). Transfer to a cutting board and allow the turkey to rest for 5–10 minutes.
Shred the turkey: Shred the cooked turkey using two forks and transfer it to a bowl. Add the BBQ sauce and stir until the turkey is evenly coated.
Assemble the flatbreads: Preheat the broiler. Place the flatbreads on a foil-lined baking sheet. Divide the BBQ turkey mixture evenly between the flatbreads and spread it to cover the surface. Top with mozzarella cheese, grilled corn, and sliced red onion.
Broil the flatbreads: Place the baking sheet under the broiler, positioning it one rack below the closest position to the heating element. Broil for 2–5 minutes, watching carefully, until the cheese is melted and bubbly. Remove from the oven and garnish with chopped cilantro. Add ranch dressing, pickled jalapeños, or hot honey if desired. Slice and serve immediately.