Heat 1 tablespoon olive oil in a large nonstick skillet over medium-high heat.
Add the chicken (drumsticks or breast fillets) and brown on both sides, about 5 minutes per side; transfer chicken to a plate lined with paper towel.
Reduce heat to medium-low and add the diced onion to the skillet; sauté until tender, about 4 minutes.
Add the minced garlic and sauté 1 minute until fragrant.
Return the browned chicken to the skillet and pour in the diced tomatoes, chicken broth, quinoa, capers, dried oregano, crushed red pepper flakes, salt to taste, and freshly ground black pepper.
Stir gently to combine, cover the skillet, and simmer over medium-low heat until the chicken is cooked through and the quinoa is tender and has absorbed most of the liquid, about 15 minutes.
Uncover, check seasoning, and serve warm.