Slice the chicken breasts in half along the length to make them thinner. Pat dry with a paper towel. Season both sides of each chicken breast with salt and pepper.
Prepare a shallow plate containing almond flour. Place each chicken breast in the flour to coat both sides and shake off the excess.
In a wide nonstick pan, add olive oil and 2 tablespoons of butter over medium heat, stirring until the butter is melted and the pan is hot.
Add chicken breasts in a single layer. Cook until each side is golden brown, about 5 minutes per side. When the chicken is cooked through, transfer to a plate. Work in batches if your pan is not large enough to hold them all at once.
Reduce to low heat. Add heavy cream, 1/4 cup lemon juice, and capers. Stir everything together, scraping up any bits that have stuck to the pan.
Increase heat to bring to a simmer. Add salt and pepper to taste. Stir in remaining 2 tablespoons of butter until melted.
Transfer the chicken back to the pan and simmer for about 5 minutes.
Remove the pan from heat. Top with chopped parsley and lemon zest. Optionally garnish with additional lemon slices. Serve while hot.