Dry the chicken breasts with paper towels, then flatten them to ½-inch thickness. Season the breasts with salt, pepper, garlic powder, and Italian seasoning. Heat olive oil in a skillet over medium-high heat. Cook the chicken for 4 to 5 minutes on each side until it reaches 165°F. Let the chicken rest for 5 minutes, then cut it into thin strips at an angle.
Lay both flatbreads on a clean surface. Brushing the outer sides of the bread lightly with olive oil will help it become crispy and golden when you cook it.
Spread 1.5 tablespoons of basil pesto on the inside of each flatbread, covering the edges for better flavor. Add a bit more pesto to the chicken before putting it all together.
Start by placing the sliced chicken on the bottom flatbread. Next, add slices of mozzarella cheese on top so they can melt. Finally, put tomato slices on the cheese. Add the top flatbread and press down lightly.
Put the assembled flatbread in a preheated panini press, a grill press, or a cast-iron skillet, and toast on medium heat. Press down firmly and cook for 3 to 4 minutes, until the bread is golden and crispy and the cheese has melted. If you're using a skillet without a press, place a heavy pan on top while it cooks. Flip it carefully after 2 to 3 minutes and press again.
Remove from the heat and let sit for 1 minute. Slice the flatbread diagonally and serve right away. Cutting it this way makes it easier to hold and looks nice.