Whisk together the lemon juice, vinegar, oregano, garlic and some salt and pepper in a small bowl. Slowly whisk in the oil until emulsified. Let sit at room temperature while you prepare the salad to allow the flavors to meld.
Rinse the quinoa in a strainer until the water runs clear. Combine the quinoa, 2 cups water, 1 teaspoon salt and 1/4 teaspoon pepper in a small saucepan, bring to a boil and cook until the water is absorbed and the quinoa is tender, about 15 minutes.
Transfer to a bowl, fluff with a fork and let sit for 5 minutes to cool slightly.
Add the almonds, olives, green onions, red onions, cucumbers, Feta and dressing and toss to coat.
Cover and refrigerate for at least 1 hour or serve at room temperature. The longer it sits the better the flavor.
If using the chicken, add the chicken right before serving.