Preheat oven to 400 degrees. Spray a large baking sheet with non-stick cooking spray; set aside.
In a small bowl, mix together the sour cream, 1 teaspoon cumin and 1/2 teaspoon lime juice; set aside.
Heat 1 tablespoon oil in a medium skillet over medium-high heat. Add in the pablano pepper, red chili pepper, onion and 1/4 teaspoon salt, and cook until they just begin to soften, approximately 3 - 4 minutes. Remove to a medium heat-proof bowl. Add in the fire-roasted peppers, olives, remaining 1 teaspoon lime juice and 1/4 teaspoon salt, mix to combine; set aside.
Thinly slice the chicken breast, pat chicken dry with a paper towel. Place chicken into a medium bowl. In a small bowl, mix together remaining 1 teaspoon cumin, smoked paprika, chili powder, garlic powder, and remaining 1/4 teaspoon salt. Add seasoning to chicken and mix together until chicken is fully coated with seasoning. To the same skillet the peppers were cooked in, heat remaining 1 tablespoon oil over medium-high heat. Add in the chicken and cook until cooked through and no longer pink, approximately 3 minutes.
Place the flatbreads onto prepared baking sheet; top evenly with the cheddar cheese. Evenly divide the chicken between the flatbreads, but only cover 1/2 of each flatbread, top chicken evenly with the pepper mixture. Place into preheated oven and bake until cheese has melted, approximately 3 - 4 minutes. Fold the cheese-only half of the flat bread over the chicken/pepper half. Secure with toothpicks, serve with cumin lime sour cream on the side and enjoy!