Blend garlic with salt in a mortar with a pestle to make a thick paste. Add pepper, chile flakes, and lemon juice and zest, mixing to blend. Stir in herbs. Drizzle in oil, whisking, until mixture becomes a loose pesto. Makes about 1 cup sauce.
Rinse fish, pat dry, then cut a few slashes into its sides, parallel to the gills. Set on a rimmed baking sheet. Rub inside and out with 1/4 cup sauce. Cover loosely with plastic wrap and let marinate at least 30 minutes and not more than 1 hour.
Brush cooking grates with an oil-soaked paper towel. Heat grill to medium heat (350° to 450°). Transfer fish to an oiled grill basket and close basket. Cook fish, turning once halfway through, until fish is opaque, about 12 minutes. Insert a thin knife or metal skewer into the thickest part of the fish and leave it for 30 seconds. Remove skewer and hold it against the inside of your wrist; it should feel warm. If it's still cool, grill fish another 2 to 5 minutes. Serve with extra sauce on the side.