Preheat oven to 375 degrees.
Spread the pesto evenly in a thin layer across the flatbreads, leaving a bit of space around the edges for a crust. Each flatbread will get about 1.5 tablespoons of pesto. Sprinkle the cheese over the pesto and then the chicken over the cheese. Add the tomatoes over the top and return the flatbreads to the oven, directly on the rack (make sure no ingredients are hanging over the edge). Bake for another 4-5 minutes until the flatbread is browned and cheese is melted.
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