Add undrained tomatoes, onion, sugar and vinegar to medium saucepan; bring to a boil. Heat over medium heat until liquid is reduced to a jam-like consistency, about 30 minutes, stirring occasionally. Remove from heat and set aside. Heat large skillet over medium heat. Add bacon and cook until crispy, about 6 minutes. Drain and set aside.
Spray cold grates of gas grill with grilling spray. Preheat grill for medium heat. Spray rimless baking sheet with grilling spray. Divide dough in half; roll each half into a 14-inch rectangle on lightly floured surface. Carefully transfer dough to baking sheet and then directly onto grill grates. Grill dough until lightly charred, about 2 minutes per side.
Spread tomato jam evenly on each flatbread; top with bacon, greens and cheese. Cut each flatbread into 5 slices.
To quickly make your own pizza dough: Add 2 cups all-purpose flour, 1 teaspoon instant yeast, 1 teaspoon salt and ½ teaspoon granulated sugar to food processor; pulse until well combined, about 15 seconds. Add ¾ cup warm water and 1 tablespoon olive oil and continue to pulse until dough forms a ball, about 30 seconds. Remove dough and knead until smooth. Place dough in medium bowl; cover and let rise until doubled in size, about 1 hour.