Season chicken with salt and pepper. Pour almond flour in a bowl and dredge both sides in almond flour, shaking off excess.
In a large skillet over medium high heat, melt 2 tablespoons of coconut oil with 3 tablespoons olive oil. When mixture starts to sizzle, add 2 pieces of chicken and cook for 3 minutes (or until browned), flip and cook other side or until browned. Remove and transfer to plate. Melt 2 more tablespoons coconut oil and add another 2 tablespoons olive oil. When this mixture starts to sizzle, add 2 more pieces of chicken and brown both sides as with the first batch. At the same time, add mushrooms and saute for 5 minutes (may need to add a tad more coconut and olive oil). Remove pan from heat, and add chicken to the plate.
In the pan, add the lemon juice, stock, and capers. Return to stove and bring to a boil, scraping up brown bits from pan for extra flavor. Taste to check for seasoning, then return all the chicken to the pan and simmer for 5 minutes. Remove chicken to a serving dish. Add 2 remaining tablespoons of coconut oil to sauce and whisk vigorously. Pour sauce over chicken and garnish with parsley.
Serve and enjoy!