Rinse greens and drain. Set aside with water still clinging to leaves.
Heat 1 1/2 tbsp. oil over medium heat in a large stockpot. Add garlic, onions, and chile flakes and cook, stirring often, until softened but not browned, about 5 minutes. Scoop half into a bowl and set aside.
Add half of greens to pot and cook, covered, until wilted, then add second half. When greens are thoroughly wilted, sprinkle with salt and toss with tongs.
Reduce heat and simmer greens, covered, until very tender, about 45 minutes, adding water occasionally if necessary to keep about 1/4 in. water in bottom of pot.
Add vinegar, remaining oil, and reserved garlic-onion mixture and toss to mix (it will be quite liquidy).
Make ahead: Chopped greens, 1 day, covered and chilled; braised greens, 1 day, covered and chilled.