In a bowl, combine the olive oil, minced garlic, cumin, coriander, paprika, turmeric, cinnamon, black pepper, salt, and lemon juice. Stir well until all ingredients meld together.
Add the chicken to the marinade, coating it thoroughly. Cover and refrigerate for at least 30 minutes.
Preheat your oven to 400°F (200°C) or heat a grill pan over medium-high heat.
Remove the chicken from the marinade, place it on a baking sheet or grill, and cook for 20-25 minutes (or 6-7 minutes per side on the grill) until properly cooked.
Let the chicken rest for a few minutes, then slice it into thin strips.
Mix together the yogurt, mayonnaise, minced garlic, lemon juice, salt, and pepper in a bowl until smooth.
Lay out the pita or flatbreads for filling.
Spread a layer of garlic sauce on each wrap.
Layer on the shredded lettuce, diced tomatoes, cucumber, red onion, pickles, and sliced chicken.
Roll the wraps tightly and cut in half if desired.