Bring 4 cups water to boiling in a large saucepan. Add potatoes; cook 5–7 minutes. Drain, pat dry, and cut into rounds 1/4-inch thick. Brush with 2 tablespoons of the oil, and sprinkle with 2 tablespoons of the horseradish.
While the potatoes are boiling coat the grill rack with nonstick cooking spray and preheat it to medium (300°F–350°F).
Grill potatoes for 10–15 minutes or until browned and tender, turning occasionally. Place the potatoes on a wire rack to cool slightly then transfer to a large mixing bowl.
Combine vinegar, remaining 4 tablespoons of oil, mustard, onion, remaining 1 tablespoon horseradish, lemon zest, parsley and red pepper flakes in a small bowl. Add to potatoes, stirring well. Serve warm or chilled.