Whisk yogurt, lemon juice, olive oil, tomato paste, garlic, cumin, coriander, salt, pepper, and red pepper flakes together in a bowl. Mix in chicken strips. Cover bowl with plastic wrap and place in the refrigerator to marinate, 8 hours to overnight.
Set oven rack about 6 inches from the heat source and preheat the oven's broiler.
Remove chicken from the bowl and arrange in a single layer on a broiling pan. Discard excess marinade.
Broil chicken, turning once, until juices run clear, about 10 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).