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Heat a 12-inch heavy skillet (not nonstick) over high heat until hot, then add oil and heat until it shimmers.
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Meanwhile, stir together flour, 1 tsp salt, and 1/2 tsp pepper, then pat veal dry and dredge in flour, knocking off excess.
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Cook veal in 2 batches, turning once, until browned and just cooked through, 2 to 2 1/2 minutes per batch. Transfer to a plate.
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Discard oil from skillet, then add butter and cook over medium heat, shaking skillet frequently, until browned and fragrant, 1 to 2 minutes. Stir in vinegar, capers, and 1/4 tsp each of salt and pepper. Return veal to skillet just to heat through, then sprinkle with parsley.
