Combine first 4 ingredients in a large bowl, stirring with a whisk. Add lettuce and next 4 ingredients (through tomatoes), tossing to coat.
Heat a large nonstick skillet over medium-high heat. Coat pan with cooking spray. Working with 1 flatbread at a time, cook bread 1 minute on each side or until toasted. Rub 1 side of each flatbread with cut sides of garlic. Arrange 1 1/2 cups chicken mixture in the center of each flatbread; roll up.