Bring 2 cups water and quinoa to a boil in a saucepan over medium heat. Simmer until quinoa is tender, 15 to 20 minutes.

Meanwhile, heat olive oil in a large skillet over medium-high heat. Saute onion until lightly browned, 5 to 7 minutes. Stir in 3 garlic cloves, chili powder, salt, paprika, and red pepper flakes with a wooden spoon. Add chicken; cook and stir for about 5 minutes. Pour in remaining 1/4 cup water. Cover and cook for 15 minutes.

Stir corn, peas, peppers, and spinach into the skillet. Cover and cook for 5 minutes more. Mix milk and flour together and pour into the skillet; cook and stir for 2 minutes.

Divide quinoa among 4 serving plates. Scoop chicken and vegetable mixture on top. Whisk lime juice and remaining garlic together in a bowl; drizzle over each serving.