1. The term "flight or fight" typically means the idea of meeting some kind of threat that one meets. Then, this person will have the choice between "flight or fight": run away from the threat or fight against the threat.
2. The term's relationship between listening as a skill means that sometimes when you're listening to bored speeches, you want to "flight", or run away. However, by attaining listening as a skill, you learn to listen to this speech, like fighting agaisnt the threat, which is "fight".
Mark Antony is repeating that line to discredit Brutus by giving examples to prove that Caesar wasn't ambitious. If Brutus was honorable man he wouldn't have killed Caesar to get what he wanted to accomplish.