In a medium pot, heat 2 cups oil to 325 degrees F.
In a bowl, toss the shallot slices with the flour. Test a shallot slice to assure the oil is sufficiently hot enough to fry the shallots. Fry them in small batches until golden brown, removing them with a slotted spoon and drain them on a paper towel. Season with salt and pepper, to taste.
Heat a large skillet, and add 1 tablespoon of oil. When the oil begins to smoke, add the Swiss chard stalks and season with salt and pepper. Cook until tender, 3 to 5 minutes. Transfer to a serving bowl. Heat the remaining oil and quickly saute the leaves until they "wilt", 1 to 2 minutes. Combine in the bowl with the stalks. Stir in the olive oil and sherry vinegar. Top with the shallots.