Mix olives, garlic, balsamic vinegar, and red pepper flakes together in a bowl.
Carefully peel tangerines and cut peels into strips. Squeeze juice from 1 tangerine over olive mixture. Add tangerine peel strips to olive mixture and toss well.
Make a packet with a large piece of aluminum foil. Pour olive mixture into packet. Arrange onion slices and rosemary over olives; drizzle with olive oil. Sprinkle fennel seeds over mixture. Fold and seal packet; place on a baking sheet.
Bake in the preheated oven until warmed, about 90 minutes. Serve warm.