Place the chicken in a medium bowl and toss with the taco seasoning. Allow to sit at room temperature for at least 15 minutes, or refrigerate overnight.
Heat a skillet to medium-high heat and add 1 tablespoon of the oil.
Cook the chicken, stirring often for 8 minutes.
Add the onion, red pepper, and chipotle chili pepper and cook for another 5 minutes.
Transfer the meat and vegetables to a clean bowl.
Reduce the heat to medium-low and carefully wipe the skillet clean.
Add the remaining 1 tablespoon of oil to the skillet.
Place the tortilla in the skillet, working in batches as necessary.
Top with the meat, vegetables, and cheese.
Add a second tortilla on top.
Cook, turning once until the tortillas are brown and crispy and the cheese is melted, about 7 to 10 minutes.
Transfer to a cutting board and cut into wedges.