Whisk together vinegar, oil, and 1/2 teaspoon kosher salt in a medium bowl. Place 2 tablespoons vinaigrette in a separate small bowl; set aside for serving. Transfer remaining vinaigrette to a squeeze bottle for basting, or leave in medium bowl if basting with a brush.
Season fillets with remaining 1 teaspoon kosher salt. Drizzle or brush with 2 tablespoons of the basting vinaigrette. Refrigerate fillets at least 15 minutes and up to 30 minutes.
Preheat grill to medium-high (400°F to 450°F). Place fish in a single layer in a metal grilling basket coated with cooking spray. Place basket on grill grate; grill, reducing heat if needed to maintain temperature of 400°F to 425°F, 6 minutes. Carefully flip basket; drizzle or brush fish directly through basket grates with 1 tablespoon basting vinaigrette. Grill until fish flakes easily when tested with a fork but doesn’t take on much color, 5 to 6 minutes. Remove basket from grill; drizzle or brush fillets with 1 tablespoon basting vinaigrette, and sprinkle with flaky sea salt. Transfer fish to a platter.