Add yogurt, olive oil, lemon juice, and spices to a large bowl. Mix together. Add whole chicken thighs and toss to coat. Marinade for 1 hour.
Once chicken is done marinating, preheat oven to 400 degrees. Place rack at the bottom of the oven. Remove chicken thighs from marinade and scrape off excess yogurt. Arrange on a vertical roasting skewer and place on a baking sheet covered in foil.
Bake in preheated oven until cooked through and chicken has started charring. Remove from oven and let cool for 10 minutes. Then, using a serrated knife, carve off chicken and place in a medium bowl.
For the tzatziki sauce:
Grate cucumber so it's in shreds. Strain to remove water. But to remove EVEN MORE water, place into a cheese cloth or paper towels and squeeze out the water. Set aside
In a medium bowl, add oil and minced garlic. Whisk quickly to help blend the garlic flavor into the oil. Do this for 1 minute. I used a mini food processor for this but if you don't have one, whisking violently in a bowl will do.
Add yogurt, cucumber, and rest of tzatziki ingredients to medium bowl with oil and garlic. Combine with a spoon or spatula. Let it sit in fridge until we prepare the wraps.
For the chicken wraps:
Take one pita flat bread and arrange about ⅓ cup of cooked chicken. Dollop tzatziki over the top, about 2 tablespoons. Sprinkle red onion, diced tomato and feta cheese over the top. Serve immediately. Repeat with other flatbreads.