Make the rub: Mix all of the ingredients in a small bowl with 2 teaspoons salt and 1 teaspoon black pepper.
Prepare the wraps: Whisk the mayonnaise and 1 tablespoon of the rub in a bowl. Cover and refrigerate until ready to use.
Preheat a grill or grill pan to medium high. Toss the chicken with 3 tablespoons rub. Oil the grill; grill the chicken until marked, about 6 minutes. Turn and grill until cooked through, about 4 minutes. Transfer 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.
Cube the chicken and arrange down the center of each piece of bread. Top with the tomatoes, onions and lettuce. Roll up and wrap with parchment paper or foil to seal.
Guy Fieri's Flatbread:
Yield:Photograph by Andrew Mccaul
Mix the flour and salt in a medium bowl. Using a wooden spoon, slowly stir in 2 cups warm water until a dough forms. Lightly flour a clean board, then turn the dough out onto it and knead until smooth, about 10 minutes. Transfer to a clean bowl and cover with a damp kitchen towel; let rest 20 minutes.
Preheat a griddle over medium-high heat. Divide the dough into 8 balls. Using a rolling pin, roll out the balls on a floured board into rough 7-by-8-inch rectangles, about inch thick. Working in batches, cook the dough on the hot griddle until marked on the bottom, 1 to 2 minutes. Flip and grill until marked on the other side. Stack the flatbreads and cover with a kitchen towel up to 20 minutes before serving.