In a small bowl whisk together the taco seasoning, salt, and pepper until combined.
Trim the chicken and slice it thinly crosswise. Pat the chicken pieces dry with paper towels and then rub the spice mixture onto all sides of the chicken pieces.
In a 12-inch nonstick skillet over medium-high heat, heat 2 tablespoons of the vegetable oil until shimmering and very small wisps of smoke start to come off of the oil. Add the chicken and cook, stirring often, until browned and cooked through about 5-7 minute. Move the chicken to a serving platter and cover with foil.
Add the remaining 2 tablespoons of vegetable oil to the skillet and heat it again over medium-high heat until the wisps of smoke start to come off of the oil. Add the bell pepper and onion and cook, stirring often, until the veggies begin to brown and they begin to brown, about 5-7 minutes. Turn off the heat, and stir in the lime juice and cilantro.
Transfer the veggies to the same serving platter as the chicken, and serve buffet style with flour tortillas, shredded cheese, sour cream, salsa, diced avocado, and lime wedges.