On a flat surface, shred chicken meat using two forks. Discard bones.
Place remaining ingredients in their own dishes in an assembly line on the table.
To assemble: hold your flatbread on your hands or on a plate. Place romaine leaves as the base to hold your chicken. Top with olives and feta cheese, drizzle with about a tablespoon of hummus dressing.
In a medium bowl, combine all ingredients. Drizzle with a little olive oil and add a little salt to taste.
Whisk hummus together with lemon juice and water; season with salt and pepper. Add an additional tablespoon of water if the dressing is to thick.