Season the salmon with ½ teaspoon salt and ¼ teaspoon pepper.
In a shallow bowl, toss the hash browns with the flour. Sprinkle them on the salmon and press gently to help them adhere.
Heat the oil in a nonstick skillet over medium heat. Add the salmon, potato-side down, and cook until the potatoes are golden brown, 3 to 4 minutes.
Carefully flip the salmon and cook until opaque throughout, 2 to 3 minutes more.
Meanwhile, in a small bowl, whisk together the sour cream, vinegar, horseradish, and ¼ teaspoon each salt and pepper.
Divide the watercress and radishes among plates, drizzle with the dressing, and serve with the salmon.