Preheat the grill to medium-high heat.
Grill the chicken breast strips until cooked through and slightly charred, about 6-8 minutes per side. Remove from grill and let rest.
Warm the flour tortillas briefly on the grill or in a pan to make them pliable.
Lay each tortilla flat and spread a generous layer of BBQ sauce over the surface.
Arrange grilled chicken strips in the center of each tortilla.
Top chicken with pineapple chunks, shredded lettuce, diced red onion, sliced red bell pepper, and shredded cheddar cheese.
Fold the sides of the tortilla over the filling and roll tightly to form a wrap.
Cut each wrap diagonally in half and arrange side by side on a white rectangular plate.
Serve with a small bowl of extra BBQ sauce on the side.