Preheat oven to 350 degrees F. Coat a 9x13 baking dish with cooking spray and set aside. Place the chicken breast halves between two pieces of wax paper and pound to 1-inch thickness using a mallet or heavy wooden spoon.
Heat the olive oil in a large skillet over medium heat. Add the almond flour, salt and pepper onto a large plate to season chicken. Mix together with a fork and spread into an even layer. One at a time, place the thin pieces of chicken into the flour mixture, ensuring the entire surface is coated.
Place the coated chicken into the skillet with the hot oil, cover, and cook for 3-4 minutes per side, or until golden brown. (Add more oil if needed.) Place the cooked chicken in a single layer in the prepared baking dish.
Add the lemon juice, chicken broth and capers to the skillet and bring the mixture to a boil, scraping up remnants from the pan. Remove from the heat and pour over the chicken in the baking dish. Bake in the preheated oven for 20 minutes.
Bake in the preheated oven for 20 minutes. Top with parsley and extra lemon slices and/or lemon juice and serve over cooked pasta or rice!