Position a rack in the center of the oven and heat the oven to 450 degrees F.
In a medium bowl, mix the tomatoes, capers, oregano, vinegar, 1/2 teaspoons salt, and 1/4 teaspoons pepper.
Season the fish with 3/4 teaspoons salt and 1/4 teaspoons pepper and dredge it in the flour, shaking off the excess. Heat the oil in a 12-inch (preferably nonstick) ovenproof skillet over medium-high heat until shimmering hot. Add the fish, evenly spaced, and cook without touching until it browns and releases easily from the pan (check by gently lifting one of the corners), about 3 minutes. Flip the fish, sprinkle the garlic around it, and cook until the garlic just starts to brown on some edges, about 30 seconds. Pour the tomato mixture around the fish and transfer the skillet to the oven. Roast until the fish is just firm to the touch and opaque when you pry open a thicker piece with a paring knife, 3 to 6 minutes.
Let the fish rest for a couple of minutes and then serve with the tomato mixture spooned over it.