In a large pot, bring the turkey wings and 6 cups of water to a boil. Turn the heat to medium-low, cover, and simmer until the meat is beginning to fall off the bone, about 1 hour. Add the collard greens, oil, sugar, chile flakes, and salt and black pepper to taste and return to a boil. Cover, turn the heat to medium-low, and simmer until the greens are tender, about 2½ hours.
Using tongs, transfer the turkey wings to a cutting board. When cool enough to handle, pull the meat and skin from the bones (discard the bones), then chop into bite-size pieces and add it back to the pot. Season to taste with vinegar and Tabasco and serve.