In a large bowl, combine olive oil, cumin, coriander, paprika, turmeric, cinnamon, cayenne pepper, minced garlic, salt, black pepper, and lemon juice. Mix well to create a marinade.
Add the chicken thighs to the marinade, ensuring they are well coated. Cover and refrigerate for at least 1 hour, or preferably overnight for better flavor.
Preheat your grill or a large skillet over medium-high heat.
Remove the chicken from the marinade and grill or cook in the skillet for about 6-7 minutes on each side, or until the chicken is cooked through and has a nice char.
Once cooked, let the chicken rest for a few minutes, then slice it into thin strips.
For the creamy garlic sauce, mix together Greek yogurt, mayonnaise, minced garlic, lemon juice, salt, and pepper in a bowl until smooth.
To serve, place sliced chicken in pita bread or flatbreads, drizzle with creamy garlic sauce, and top with sliced cucumbers, tomatoes, and red onions.