In a large pot, combine smoked turkey, broth, onion, and garlic. Bring to a boil, then reduce heat and simmer, covered, 35–40 minutes.
Remove turkey, let cool slightly, then shred the meat off the bone and discard skin and bones.
Return shredded turkey to the pot along with collard greens, vinegar, and red pepper flakes.
Simmer, uncovered, 15–20 minutes, until greens are tender.
Season with salt and pepper to taste and serve hot.