Cook pasta in a large pot of boiling salted water until tender to the bite, 9 to 12 minutes or according to package instructions. Drain and set aside.
Meanwhile, toss shrimp with 2 tbsp. olive oil, onion, garlic, 3/4 tsp. salt, chile flakes, and cumin; marinate at room temperature 10 minutes. Preheat a medium frying pan over medium heat, then add shrimp and marinade. Cook, stirring often, until shrimp are pink and firm, 3 to 4 minutes.
In a large bowl, toss together pasta, shrimp mixture, spinach, chickpeas, yogurt, mint, lemon juice, remaining oil, and lemon zest. Season to taste with salt. Serve warm or at room temperature.
Note: Nutritional analysis is per serving.