In a large skillet over medium-high heat, heat oil. When oil is hot but not smoking, add salmon skin-side up and season with salt and pepper. Cook salmon until deeply golden, about 6 minutes, then flip over.
Add wine, juice of 1 lemon, garlic, and red pepper flakes. Bring to a simmer and cook, basting salmon occasionally with a spoon. When salmon is opaque, remove from skillet. Add butter and remaining lemon juice to pan and whisk to combine with the sauce. Let simmer until thickened slightly, 2 minutes.
Serve fish drizzled with pan sauce and topped with fresh lemon slices and dill.
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