In a small bowl whisk together lemon juice, Dijon, 2 tablespoons olive oil, anchovy paste, Worcestershire sauce, garlic, salt, and pepper. Stir in ¼ cup parmesan cheese.
In a small bowl combine salt, pepper, garlic powder, and onion powder. Season the chicken breasts on both sides with the spice mixture. Heat an outdoor grill to medium-high heat. Add the chicken breasts and cook for 6-7 minutes per side or until fully cooked (the internal temperature has reached 165 degrees F.). Remove from the grill to a plate and let rest.
Turn the heat on the grill to medium. Add the flatbreads and cook for 1-2 minutes being careful not to burn them. Remove from the grill.
Slice the chicken breasts into thin strips. In a large bowl combine romaine lettuce, sliced chicken Caesar dressing, ¼ cup shredded parmesan cheese. Spoon over the flatbreads. Slice and serve.