Dredge snapper fillets in flour. Tap off excess. Sprinkle with salt and pepper, and set aside.
Heat 3 tablespoons olive oil in a large skillet over medium-high heat. Place half the fillets, flesh side down, in skillet, and cook until golden brown on both sides, 4 to 5 minutes total. Remove fish, and transfer to a large flat dish. Add 3 tablespoons oil, and repeat cooking the remaining snapper. Remove from the skillet; set aside.
Add remaining 2 tablespoons oil to skillet; reduce heat to medium. Add garlic; cook, stirring, until lightly browned, about 30 seconds. Stir in tomatoes and wine; season with salt and pepper. Divide mixture evenly between two large skillets; let simmer over medium-low heat until sauce thickens, 20 to 30 minutes.
Divide parsley between skillets. Place half the fillets, skin-side down, in each skillet, and simmer until the fish is cooked through, 6 to 8 minutes. Remove from heat, and serve immediately.