Shred the cooked chicken breasts using two forks or a stand mixer until finely pulled apart.
Transfer the shredded chicken to a large mixing bowl. Add the sweetcorn, chopped red onion, cream cheese, barbecue sauce, grated cheese, and season with salt and pepper. Stir thoroughly until the ingredients are evenly combined into a cohesive filling.
Spoon the filling into the centre of each wrap, distributing it evenly among the four tortillas.
Fold in the sides of each wrap, then roll tightly from the bottom upwards to enclose the filling.