Pierce sausages with a fork (in a few places). Grill for 8 minutes or until cooked through. Set aside and allow them to cool. Then cut into slices.
Heat oil in a large skillet over medium high heat. Add onions and sauté until golden brown, then add peppers. Continue to cook, stirring often, for about 10 minutes. Once peppers are tender, add vinegar, wine, and sugar. Reduce heat and simmer until liquid is almost all absorbed, about 3–5 minutes. Season with salt and pepper to taste.
Brush flatbread crusts lightly with olive oil and grill, oil side down, until heated through and marked with grill marks.
Place flatbreads on a serving board and sprinkle half your cheese overtop. Then add sausage, peppers, and onions. Sprinkle the rest of your cheese over toppings, then slice and serve.