Mix cranberries, maple syrup, shallot, thyme and salt in an 8x8 inch baking dish. Roast, stirring once or twice, for 15 minutes. Set aside.
Lay flatbreads out on work surface. Spread the hot cranberry mixture over the flatbreads. Top with the goat cheese. Bake directly on the oven rack until the cheese is softened and flatbread is crispy, 8 to 10 minutes. Cut into 8 small wedges or strips and serve.