Slice the chicken breasts in half to make thinner cutlets (cut them hamburger-style).

On a plate, combine the gluten-free flour, thyme, garlic powder and sea salt and stir well.

Rinse each chicken cutlet with water, then transfer to the plate with the flour mixture. Dredge the chicken in the flour mixture and transfer to a plate.

Preheat the oven to 225 degrees F.

Heat the avocado oil over medium-high heat in a large non-stick skillet. Wait a few minutes while the oil heats up.

Place two of the chicken cutlets into the hot skillet and cook 3 to 5 minutes per side, until golden-brown on each side. Be sure the chicken has plenty of room for even cooking. Transfer to a plate. Repeat for the remaining chicken, then transfer the plate of chicken to the preheated oven. This is to keep the chicken warm while you're preparing the sauce. You want the internal temperature of the chicken to reach 160 to 165 degrees F.

Keeping the skillet you used to cook the chicken on the stove top, reduce the heat to medium or medium-low. Add the wine, lemon juice, and capers. Stir well and allow sauce to come to a full boil. Continue cooking sauce until it thickens and is reduced by half its original volume.

Remove sauce from heat and stir in the butter until melted.

Serve the chicken with the caper sauce poured over it with your choice of side dishes.