Preheat oven to 350°F. Mix tomato sauce, vinegar, brown sugar, raspberry jam and seasonings in medium saucepan on medium heat. Bring to boil. Reduce heat to low; simmer 20 minutes or until barbecue sauce is slightly thickened.
Mix chicken and 3/4 cup of the barbecue sauce in medium bowl. Spread 1 tablespoon of the remaining barbecue sauce on each flatbread. Top evenly with chicken mixture and cheese. Place flatbreads on baking sheets.
Bake 15 minutes or until cheese is melted and bubbly.