Set a skillet over medium heat and add shredded chicken with BBQ sauce. Stir until well-coated and simmer for 3 to 4 minutes until small bubbles form around the edges and sauce thickens slightly. If using raw chicken, cook in oil for 6 to 8 minutes until internal temperature reaches 165°F, then add BBQ sauce.

In a large bowl, combine shredded cabbage and grated carrots. In a smaller bowl, whisk together mayonnaise, apple cider vinegar, salt, and pepper until smooth. Pour dressing over vegetables and mix until lightly coated. Let coleslaw rest for 10 minutes at room temperature so cabbage softens while staying crisp.

Warm each 10-inch tortilla in a dry skillet for about 15 seconds per side until soft and flexible. Lay tortilla flat and spoon generous portion of warm BBQ chicken down the center, staying about 2 inches from each edge. Add hearty handful of coleslaw on top of chicken.

Fold left and right sides of tortilla inward about 1 to 2 inches to create flaps. Starting from bottom edge, roll tortilla up and over filling while keeping firm pressure. Tuck as you go to create tight wrap without squeezing filling out the ends. Slice each wrap in half diagonally and arrange on serving platter.