Peel potatoes and put in a pot with cold, salted water to cover. Cover pot and bring to a boil. Lower heat and simmer, uncover, and cook until done, about 25 minutes. Drain, reserving cooking liquid. Break up the potatoes with a potato masher (they should be quite lumpy, not smooth). Meanwhile, cook the bacon over low heat until crisp, turning often. Drain and chop into 1/2 inch chunks. Pour off all but 2 TBS of the bacon fat, and, reserve extra fat. Stem and chop the kale. Mince the garlic. Put half the kale and half the garlic into the frying pan. Season with salt and pepper and cook over medium heat until kale is wilted, about 1 minute.
Transfer to a bowl. Repeat using more bacon fat as needed. Return all kale to the fry pan and add the heavy cream. Simmer over very low heat until the kale is tender, about 10 more minutes. Combine potatoes with about 3 cups of the potato cooking liquid and 1 cup of the chicken stock. Add more stock if needed to get a good consistency. Add kale mixture (with the bacon) to the pot and bring to a simmer. Season to taste with the vinegar and salt and pepper. This is up to you as to how much vinegar you use. Mince the chives or green onions and place in an extra bowl to top the soup.