Question: I think the most natural party organization for a group of friends that are playing a game is a flat one, in which no one has authority over another, and decisions are made by consensus (and if that fails, with votes).

But there are times when the setting implies that the party should have a leader. In theory that shouldn't be a problem, as roleplaying is about portraying people who are not yourself, be they a noble or a servant, but in practice not everyone is okay being subordinate to another even if it's fictitious.

I have been in games in which leadership went smoothly, because everyone accepted the leader. But I have been in others in which players had a hard time accepting the leader, and every decision and step was an argument.

What are the keys to successfully including a leadership role in a party? How should the leader lead and the followers follow?

Answer: 
While some groups may accept an authoritarian structure, my experience has been that, for most groups, it is better to recognize that, even though one *character* is in charge in-game, all of the *players* are still equal out-of-game. So you and I would still be able to discuss plans or decisions out of game, even if my character must obey your character without question in game.
Games are a great way to teach complex subjects. Have you considered using a setting where the player characters are in a hierarchical organization? 

I learned how to handle this as a GM and player from playing FASA *Star Trek* and *Twilight 2000*. In *Star Trek*, sometimes I would play as a Captain and lead the Crew on a mission and other times I'd play as a Lieutenant and follow orders. Constraints like having to follow orders can present great roleplaying and creative opportunities.

If you are worried about how a particular player would handle it, consider experimenting with it in the fiction. Using *Star Trek: The Next Generation* as an example, let's say someone is playing Lt. Barclay. He's not a good leader, but the senior staff wants him to improve. 

So, Lt. Barclay is given command of an away team. Riker mentors him through picking a balanced team and making sure the Lt. is set up for success -- picking experienced away team members for a mission with a high probability of success. Riker models being a good follower and Barclay learns to handle team leadership. Then, the Crew and Lt. Barclay debrief and discuss the mission.

By extension, the players learn how to handle the table dynamic at the same time.