Place the mayonnaise, sriracha and lime zest in a small bowl, mix to combine; set aside.
Heat 1 tablespoon olive oil in a large skillet over medium-high heat. Add in the poblano pepper, red bell pepper, onion, 1/2 teaspoon salt and 1/4 teaspoon black pepper and cook until peppers and onion are softened, approximately 10 minutes.
Pound chicken to flatten to 1/2-inch thickness. Cut into 1-inch by 3-inch strips; set aside.
Place the flour, cumin, chili powder, remaining 1/2 teaspoon salt and remaining 1/4 teaspoon black pepper into a resealable plastic zip-top bag and shake to combine. Add in the chicken and toss to fully coat chicken in flour mixture.
Heat 2 tablespoons oil in a large skillet with a lid over medium-high heat. Add in the chicken pieces, in one layer, and cook until golden brown and chicken is cooked through, approximately 3 minutes per side; remove from skillet and set aside.
Wipe skillet out and place back over medium heat. Add in 1/2 tablespoon olive oil and heat. Place one of the flat breads into skillet and cook until warmed, approximately 1 minute, flip bread over. Top half of the bread with half of the cheddar cheese, half of the chicken, half of the peppers and onions and half of the chipotle gouda cheese and cover skillet with lid to allow cheese to melt, approximately 1 - 2 minutes. Remove from skillet, spread half of the sriracha lime aioli on the uncovered half, sprinkle with half of the cilantro, then fold over covered half, secure with a toothpick. Prepare the second flat bread in the same manner using remaining ingredients and enjoy!!