While leadership can lead to authority, leadership relationships unlike authoritative ones can arise consensually among piers. I don't think there's anything inherent to the concept of a leader (in the sense of one who guides by going first) that is dependent on hierarchy.
If you want to lead and no one wants to follow then you go alone. If you need the authority to force people to follow you, well.. that's more about desire for power than desire to reach stated goals.
The thing to understand is that flat management is step backwards. Every unit in community should utilize their skills. Management IS a skill. So natural leaders should be leaders. Natural organizers should be organizers and so on.
Problems are starting when artificial system is created where people are being valuated based on some idiotic scoring system instead of individual skill review.
Democracy - the system closest to it is being picked as best in the world as any other system attracts tyrants that gather unlimited power in their hands. Yet it still have leaders.
Getting rid of leaders is causing confusion and most companies that claim they have no managers will still have them, but under different name, like team leaders, project supervisors etc.