Heat oil in a large pot or Dutch oven over medium-low.
Add fennel, onion, garlic, salt, black pepper, and red pepper flakes, and cook until softened, about 5 minutes.
Stir in oregano and cook 30 seconds.
Stir in tomatoes with their juices and broth, bring soup to a boil then reduce to a simmer and cook for 10 minutes.
Stir in kale, simmer 10 minutes.
Stir in chickpeas and vinegar and simmer 5 minutes. Season soup with additional salt, pepper flakes, and vinegar to taste.
Drizzle servings with olive oil and top with chopped fennel fronds.