Season salmon with salt and pepper, then coat in flour, shaking off excess.
Heat oil in a large skillet on medium-high. Cook salmon until golden brown, 2 to 3 minutes per side. Reduce heat to medium, add garlic, and cook, stirring, 1 minute.
Add wine, lemon juice, and capers and simmer until fish is just opaque throughout, 5 to 6 minutes. Remove from heat, add butter and parsley, and stir to melt, 30 seconds. Serve with lemon slices if desired.