Cook polenta with salt as package directs.
Meanwhile, cook bacon in a large frying pan until crisp. Transfer to paper towels.
Discard fat from pan. Heat oil in same pan over medium heat. Cook shallots, garlic, and chard ribs until softened, 4 minutes. Stir in chard leaves, chile flakes, and 1/3 cup water. Cover, reduce heat to low, and cook until wilted.
Stir butter and cheese into polenta and spoon into bowls. Toss chard with vinegar and spoon over polenta. Crumble bacon and sprinkle on top.