Season salmon fillets with salt and pepper. Pour flour in a bowl and dredge salmon, shaking off the excess.
Heat oil in a skillet over medium heat and cook salmon fillets until browned on both sides, about 3 minutes per side. Transfer to a plate and keep warm.
Pour wine into the skillet and scrape browned bits from the bottom. Add garlic and cook until garlic is fragrant and slightly brown and liquid is reduced by half, about 1 minute. Add chicken broth, lemon juice, and capers. Bring to a boil while stirring. Stir in butter until melted. Return salmon fillets to skillet and spoon sauce over them.
Cook, turning fillets once, until salmon is cooked through and flakes easily with a fork, about 4 minutes. Serve salmon with sauce poured over it and garnish with lemon slices.
