Cook chicken if needed: simmer in lightly salted water until 165°F, 12–15 minutes. Cool, then chop or shred.
Whisk yogurt, mayonnaise, olive oil, lemon juice, Dijon, garlic, salt, pepper, and red pepper flakes in a bowl.
Dice celery, onion, and cucumber. Halve the tomatoes. Chop dill and parsley.
Combine chicken, celery, onion, cucumber, tomatoes, and olives in a large mixing bowl.
Pour in the dressing and toss until everything is evenly coated.
Fold in the feta gently so some crumbles stay intact.
Chill for 15 minutes to meld flavors. Serve in pita, lettuce cups, or over greens.