Lightly grease the slow cooker with cooking spray or a little olive oil.
In a small bowl, whisk together the olive oil, lemon juice, garlic, cumin, paprika, coriander, turmeric, cinnamon, onion powder, salt, black pepper, and cayenne.
Place the chicken thighs into the slow cooker and pour the spice mixture over the chicken. Turn the chicken to coat evenly.
Cover and cook on LOW for 5 to 6 hours or HIGH for 3 to 4 hours, until the chicken is tender.
Remove the chicken from the slow cooker and shred it using two forks.
Return the shredded chicken to the slow cooker and stir it into the cooking juices. Let it sit for 10 minutes so it absorbs the flavorful sauce.
Warm the tortillas or pita bread.
Fill each wrap with the chicken, lettuce, tomatoes, red onion, pickles, and a drizzle of garlic sauce or tzatziki.
Serve immediately.