Place chicken breast halves between pieces of plastic wrap. Using the flat side of a meat mallet, pound each to 1/4-inch thickness. Sprinkle chicken with lemon-pepper seasoning.
In a very large skillet heat oil over medium-high heat. Add chicken in batches; cook 2 to 3 minutes per side or until chicken is no longer pink in center (165 degrees F). Transfer to a cutting board; let stand 2 minutes. Cut into strips. Carefully wipe skillet dry.
Add flatbreads in same skillet; toast over medium-high heat 1 to 2 minutes each side.
In a small bowl combine hummus and yogurt. Spread on flatbreads. Top with chicken, tomatoes, cucumber, onion, and feta. Sprinkle with parsley, if desired.