Melt 1 tablespoon butter and 1 tablespoon oil in an oven-safe skillet, and place the chicken thighs skin side down. Sear on both sides until golden brown, for about 2-3 minutes on each side.
Melt remaining 1 tablespoon of butter and oil each, and add the garlic and red pepper flakes, and cook for 1-2 minutes, stirring frequently, until fragrant.
Return the chicken thighs to the skillet, and place in the oven and bake until the chicken thighs are cooked through. This will take about 25-30 minutes.