Preheat the broiler. Whisk the yogurt, 2 1/2 tablespoons olive oil, the lemon juice, garlic, 1/4 teaspoon salt and the cayenne in a large bowl. Add the kale and toss to coat; set aside at room temperature while you prepare the shrimp.
Toss the shrimp with the remaining 1/2 tablespoon olive oil on a baking sheet. Broil until just cooked through, 4 to 5 minutes; let cool slightly.
Add the shrimp, chickpeas, tomatoes and red onion to the bowl with the kale; toss to coat. Stack the pitas on a plate and warm in the microwave, about 30 seconds. Fill with the shrimp-kale mixture.