In a large mixing bowl, combine the shredded chicken with the Hawaiian BBQ sauce. Stir well to ensure that each piece of chicken is thoroughly coated with the sauce.
Prepare your fresh vegetables: thinly slice the red bell pepper and dice the fresh pineapple. In a separate bowl, combine the diced pineapple, sliced red bell pepper, shredded carrots, and finely shredded red cabbage. Toss the mixture gently, then season with a pinch of salt and pepper to enhance the flavors.
On a clean, flat surface, lay out one tortilla. Spoon approximately ½ cup of the BBQ chicken mixture into the center of the tortilla, spreading it slightly to create an even layer.
Add a generous portion of the mixed vegetables on top of the chicken. Follow with a few slices of avocado and a sprinkle of fresh, chopped cilantro to brighten the dish.
To form the wrap, fold the bottom edge of the tortilla over the filling, then fold in the sides before rolling it tightly from the bottom to the top. Ensure the filling is securely wrapped inside.
Repeat this process for the remaining tortillas and filling until all wraps are prepared.
For an added crispness and flavor boost, preheat a skillet over medium heat. Grill each wrap for 2-3 minutes on both sides, or until they are slightly crispy and heated through.
To serve, slice each wrap diagonally in half and arrange them on a plate. Garnish with lime wedges on the side for a zesty kick!