Place the salt and water into a 4-quart container and stir until the salt has dissolved, 1 to 2 minutes. Add the trout fillets, making sure they are submerged. Cover and refrigerate overnight.
Combine the water, vinegar, sugar, cloves, allspice, peppercorns, bay leaves, and red pepper flakes in a 2-quart saucepan set over medium-high heat. Cook, stirring occasionally, until the liquid comes to a boil, approximately 5 minutes. Cool to room temperature and then refrigerate overnight.
Remove the trout from the brine and rinse thoroughly under cold running water for 1 minute. Submerge the fillets in clean, cold water and refrigerate for 1 hour.
Drain and rinse the fillets. Pat dry. Lay the fillets in a single layer, skin-side down, and brush each with mustard. Place a cornichon or a pickled onion on the fillet, roll it up, and secure with 1 or 2 toothpicks. Alternate layers of rollmops and thinly sliced onion in a glass jar or ceramic crock.
Pour on the chilled pickling mixture, cover, and refrigerate for at least 5 hours and up to 2 days. Drain and serve chilled with crusty bread.