Wash the collard greens well in a sink of cold water. Cut out the thick stems and chop the leaves into 1-inch strips.
In a large pot or Dutch oven, cook the bacon over medium heat until crisp, about 6 minutes.
Add the onion and cook until soft, about 5 minutes. Stir in the garlic and red pepper flakes and cook for 30 seconds.
Add the broth and bring it to a boil. Add the greens a few handfuls at a time, stirring as they wilt.
Cover, lower the heat and simmer for 45 minutes to 1 hour, stirring now and then, until the greens are silky and tender.
Stir in the vinegar, sugar, salt and pepper. Taste and adjust, then serve with some of the cooking liquid.