Rinse the scallops in cold water and pat dry with paper towels. Remove the stems from the mushrooms and reserve both the stems and caps. Brush a shallow (8- to 9-inch diameter) baking dish with 1 tablespoon of olive oil; preheat the oven to 350 degrees.
Toss the scallops with the flour and arrange them with the mushroom caps in a single layer in the dish. Pour the wine into the dish along the edge. Finely chop the mushroom stems and mix them with the bread crumbs, onion, parsley, garlic, pepper flakes and salt. Sprinkle this mixture over the scallops and mushrooms. Drizzle with the remaining olive oil.
Bake in the heated oven until the mushrooms are soft and scallops are cooked through, about 30 minutes. Serve warm, or cover and refrigerate up to 24 hours.
To reheat, loosely cover with foil and bake for about 45 minutes in a 350 degree oven.