Heat the olive oil in a large skillet over medium-high heat until shimmering.
Season the chicken breasts evenly with kosher salt and black pepper on both sides.
Add the chicken breasts to the skillet and cook for 5-6 minutes on each side, until golden brown and cooked through (internal temperature should reach 165°F). Remove chicken from skillet and set aside on a plate.
Reduce heat to medium and add the minced garlic to the skillet. Sauté for 30 seconds until fragrant, stirring constantly to prevent burning.
Pour in the chicken broth, lemon juice, and add lemon zest, dried oregano, and crushed red pepper flakes. Stir to combine and bring the sauce to a simmer.
Add the cherry tomatoes, baby spinach, and sliced red onion to the skillet. Cook for 3-4 minutes, stirring occasionally, until the vegetables are just tender and the spinach is wilted.
Return the cooked chicken breasts to the skillet, spoon some sauce and vegetables over the top, and cook for an additional 2 minutes to heat through and meld flavors.
Sprinkle the chopped fresh parsley over the skillet before serving.