Pat salmon dry. Season both sides with salt and pepper, then dust lightly with flour and shake off excess.
Heat olive oil and 1 tbsp butter in a large skillet over medium-high heat until shimmering.
Sear salmon, skin-side down first, 3–4 minutes per side until just cooked through. Transfer to a warm plate.
Lower heat to medium. Add remaining 2 tbsp butter, then sauté shallot until soft, about 1 minute. Stir in garlic for 30 seconds.
Pour in wine and simmer, scraping browned bits, until reduced by about half, 2–3 minutes.
Stir in broth, lemon juice, capers, and red pepper flakes. Simmer 2 minutes to meld flavors.
Whisk in cream and lemon zest. Simmer gently until slightly thickened and glossy, 2–3 minutes. Season to taste.
Nestle salmon back into the pan and spoon sauce over the fillets. Warm through for 1–2 minutes.
Finish with parsley and an extra squeeze of lemon if you like. Serve right away.