Preheat oven to 400°. Place chicken on a foil-lined rimmed baking sheet. Rub with oil and season with salt, pepper, and pepper flakes. Bake 15 to 20 minutes, until juices run clear when pierced with a knife or temperature registers 165° on a meat thermometer. When cool enough to handle, cut chicken into 1/2-inch-thick slices.

Meanwhile, turn a stove burner to high heat. Place bell pepper on burner and roast 12 to 15 minutes, turning regularly with tongs so pepper chars evenly. Place in a paper bag; seal and let stand (and steam) 5 minutes. Peel off blackened skin and discard. Cut pepper into quarters; remove and discard seeds and core.

Open sandwich loaves and spread about 1 Tbsp. pesto on each slice. Top the bases of each loaf with Fontina, red pepper, arugula, chicken, and another slice of Fontina, dividing evenly. Place tops on sandwiches.

In a preheated panini maker, press sandwiches for 6 minutes or until heated through. Alternatively, preheat oven to 400°. Place sandwiches on a baking sheet and bake about 6 minutes. Serve immediately.