In a mixing bowl, whisk together the olive oil, Greek yogurt, lemon juice, chopped garlic, cumin, coriander, smoked paprika, turmeric, cinnamon, red pepper flakes (if desired), salt, and pepper until well blended.
Place the chicken thighs into the marinade, ensuring they are fully coated. Cover the bowl with a lid or plastic wrap and let it marinate in the refrigerator for a minimum of 1 hour, or overnight for deeper flavor.
Heat a grill or a large frying pan over medium-high heat. If using a frying pan, add a splash of olive oil to avoid sticking.
Take the marinated chicken out of the bowl, allowing any excess marinade to drip off. Cook the chicken on the grill or in the pan for about 6-7 minutes on each side, or until the chicken is cooked through and has a golden-brown exterior.
Once the chicken is done, transfer it to a cutting board and allow it to rest for 5 minutes. Slice the chicken into thin strips.
Assemble the wraps by placing the sliced chicken in pita or flatbreads, and top with your choice of diced cucumbers, chopped tomatoes, sliced red onion, shredded lettuce, and a generous drizzle of tahini or garlic sauce.