After choosing the result of the coin toss, you find yourselves separated into three teams.
Choose a Fragment
After some cutscenes, each team has a new fragment unlocked. You can see these fragments in the Flow menu. You can play through these fragments in any order.
In each team's Execution fragment, you will be prompted to ask three questions. You have to ask all three before the cutscene will finish.
Afterward, you will be required to vote for one of the other two teams. You can vote however you wish. Your vote will be followed by a cutscene.
Play All Three Fragments
In order to advance the story, be sure to play all the way through all three fragments, and be sure to vote at the end.
Choose a New Fragment
New fragments will unlock in the Flow menu after all three teams have voted. You can choose any of these to continue the game.
Changing the Outcome
As you saw in the Coincide fragment, you can use the Flow menu to go back and make a different decision. This is also true of the Execution votes. To change the result of the voting, go into the Flow menu and jump to the Execution Vote. The game remembers the most recent votes, so changing one team's vote can change the result. But if you don't remember what the last votes were, just make all three teams vote again. Once all three teams have voted again, the new outcome will be unlocked (assuming you had the teams vote differently from before).
To do this in the minimum number of steps, you should kill a team with your first three votes. Then change a vote so that all teams survive. Then change a vote to kill one of the unkilled teams, and finally change a vote to kill the last unkilled team.
Unlock all Four Outcomes
You might find yourself unable to progress in the game if you do not unlock all four outcomes on your flow chart, so you might want to do so before proceeding.