Heat the grill to medium, 325 F. Brush both sides of the flatbread with olive oil and place on the grate. After one minute, turn the flatbread and spread a layer of pesto over the top.
To the flatbread, add the chicken, sun-dried tomatoes, basil, oregano, red pepper flakes and season with salt and freshly ground black pepper. Spread the Mozzarella and Feta evenly over the top.
Spread the toppings to 1/2 inch away from the edges, close the lid and grill for 3 – 4 minutes or until the cheese is melted, watching that the bread doesn’t burn. If you want a longer cooking time, use a pizza stone or baking sheet on the grill.