In a small bowl mix all of the ingredients together with 1 1/2 teaspoons salt and 1 teaspoon pepper.
For the wraps:
Whisk the mayonnaise with 2 teaspoons of the rub in a bowl. Cover and refrigerate until ready to use.
Preheat a grill or grill pan to medium high heat. Toss the chicken with 3 tablespoons of the rub. Oil the grill and grill the chicken until marked, about 6 minutes. Turn and grill until chicken registers an internal temperature of 165°F. Transfer chicken to a cutting board.
Wipe the grill clean and brush with more oil. Lay the bread on the grill, then brush with the spiced mayonnaise and top with mozzarella. Grill until the bottom is marked, 1 to 2 minutes. Transfer to a cutting board.
Cut the chicken into cubes and divide among flatbread pieces, arranging down the center of each piece. Top with the tomatoes, onion, and lettuce. Roll up and wrap with parchment paper or foil to seal.