On your countertop, lay out a sheet of parchment paper at least 15 inches long and top it with a slightly longer layer of plastic wrap.
Lay out your fillets of salmon, tails away from you. Overlap the fillets of flounder about 1 inch over the tails of the salmon. Place the scallops on a metal skewer and set at the end of the flounder furthest from you. Season the seafood with the salt and pepper and sprinkle with the herbs.
Using the plastic wrap, roll the fish towards you so that the plastic begins to pull the flounder over the scallops. Be sure not to roll the plastic into the fish roll. Use a half sheet pan to push the roll tight as you pull the plastic toward you. The roll should be tight and you should be able to remove the sheet of plastic. Then, roll the fish in the parchment away from you so it is completely encased in the parchment, like a sausage, twisting the ends slightly. Refrigerate for 1 hour.
Make the compound butter: In a large bowl, use a wooden spoon to mix the butter, parsley flakes, salt, and pepper. Place the mixture on a piece of parchment and fold the parchment over itself. Pull to form a roll and twist the ends. Place in the freezer for 10 minutes to set up. Slice into 1/4-inch rounds and remove the parchment.
Heat your broiler and place the oven rack 6 inches from the heating element. Brush a broiler pan with oil.
Remove the metal skewer and, using the electric knife, slice the roulade into 3/4- to 1-inch-thick rounds. Place onto the prepared broiler pan, remove the parchment paper, and brush each round with oil. Broil until the rounds reach an internal temperature of 130°F, 6 to 9 minutes.
Serve with 1 slice of compound butter on each fish roll.