Cut the chicken breasts into long, thin strips so they cook quickly and evenly.
In a small bowl, combine the olive oil, buffalo wing sauce, smoked paprika, garlic powder, and salt.
Add the chicken strips to the marinade and toss until evenly coated. Let the chicken marinate for at least 10 minutes or up to 24 hours in the refrigerator.
Heat a large non-stick skillet over medium-high heat.
Add the marinated chicken strips to the skillet and cook for about 4–5 minutes, turning as needed, until the chicken is fully cooked and no longer pink in the center.
While the chicken cooks, arrange the tortillas on a clean plate or work surface.
Add lettuce, ranch dressing, shredded carrots, red onion, and cheddar cheese to the center of each tortilla.
Place several cooked chicken strips over the vegetables.
Fold the sides of the tortilla inward, then roll it tightly from the bottom to form a burrito-style wrap.
Slice in half and serve immediately with extra buffalo sauce or ranch dressing, if desired.