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: 
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.
I find that a related problem is that players are a lot smarter than their characters. They will also take 15 minutes in Real Life to debate whether to open the chest. And so you have to decide: are you playing to min/max and get the loot or are you there to focus on fun and roleplaying? (Neither is right nor wrong, but I find when it comes to Monty Hauling, good tactics is always the leader and there's no problem.)

So if you're focusing on role-playing style and a leader...

I have found the solution to this problem (over analyzing in the meta) is arrived at through good role-playing. Make the party leader the Paladin and give the Paladin to "that guy" in the group (you know the one I mean) who leads by his station. Encourage the players to respect his social position, but talk behind his back. Make sure they make decisions in a game-timely-manner. In short, make the *characters* experience interpersonal conflict and not the players.

It takes a little effort to switch gears, but some of the most hilarious moments I have had were when the *characters* bickered. Once, I (as DM) said, "In the middle of the room is a pillar with a giant chest on top, laden with gold. A mysterious magical light casts a luminous glow around it from above—" The impulsive rogue, interrupting my description of the room, picked up his 20 sider. Player #2 yelled (in character) "DUCK!" and he was so into the game he almost threw player #3 out of his chair onto the floor out of instinct. 

So long as the DM honors the unwritten contract "try not to kill the players," not going along with the group can add to the experience. I find most players start to understand the unwritten code of things, like "If I run off in this direction, we separate the party and then it's half as fun for everybody." So they stop doing that. Most people can find the right way to be just rebellious enough to not ruin it.

Another time the party was getting wrecked by this Hydra growing heads. So the Sorcerer said, "I'm dropping lightning bolt." I pointed out the old school lightning bolt+water=fireball rule and warned him the entire party (which foolishly charged into the water) would also get zapped. The whole table held its breathe as he considered it briefly and said "we gotta kill this thing." He literally saved the entire party from a wipe, but no character ever forgot that Mork thought they were expendable, even when that's not the truth of the situation. That's Epic story right there.

The best part is I didn't plan a second of it. They rush in, made a bad situation worse, and he pulled it off—and they never forgave him. Ah the memories.