Remove skin and large bones from salmon. Combine in a bowl with 1/2 cup of the bread crumbs, mayonnaise, egg, Worcestershire sauce, capers, and tarragon, and season with salt and freshly ground pepper. Mix together well and form into 12 small patties. Coat salmon patties in remaining bread crumbs. Cook rice according to package directions. Leave covered and set aside while you cook the salmon cakes.
Heat the vegetable oil in a large, nonstick skillet over medium-high heat until oil is hot but not smoking. Sauté patties in batches for 2 to 3 minutes on each side, or until golden brown. Toss rice with the parsley, olive oil, lemon juice, and kosher salt to taste. Serve with salmon cakes and lemon slices.