Preheat the oven to 425°F and line a large sheet pan with parchment paper.
Toss chicken strips with grated garlic, olive oil, lemon juice, cumin, smoked paprika, kosher salt, curry powder, and black pepper.
Spread chicken on the sheet pan, add bell peppers, then drizzle peppers with olive oil and season lightly with salt.
Roast for 16 to 20 minutes, stirring once, until the chicken reaches 165°F and the peppers are tender.
Mix Greek yogurt, squeezed grated cucumber, lemon juice, olive oil, grated garlic, dried dill, kosher salt, and pepper.
Prepare the diced cucumber, red onion, kalamata olives, feta cheese, and warm flatbread.
Fill each flatbread with chicken, peppers, yogurt sauce, cucumber, onion, olives, and feta, then serve warm.