Being chill is a state of mind, there isn't a step by step process to achieve it. For example, consider "be positive", you can only discuss it in generalities. Just like being positive can be described in terms of searching out and focusing on the good in any situation, being chill is about not allowing something to take you out of the moment unnecessarily.
Getting irritated because someone tells you to chillout is a good example of allowing yourself to be taken out of the moment for no practical reason. What it boils down to is experiencing less happiness. When you're reacting to something in a negative or defensive manner, you're not enjoying whatever you would be experiencing if you had been more relaxed.
Sometimes in life you have to be taken out of the moment to react to something, consider being confronted by an aggressive rabid dog while making out with a cutie on a park bench, sure you could chill and not let the situation distract you from what you would be experiencing otherwise, but there might be uncomfortable consequences. Alternatively, if you're enjoying said makeout and some dude yells 'get a room!', well, you can choose to get irritated, maybe you even shout back 'fuck you' or something similar, but you've let something affect you and pull you out of an experience that makes you feel good.
What's worse, in social interaction one person's reaction or lack thereof can have a powerful effect on those in his or her company. Essentially when you shout back at the mouthy dude, you're not just letting yourself get taken out of the moment you're pulling your lady out of it to. This is a simplification, obviously she decides to some extent how to react, but in my experience what you do is going to have a major impact on how she feels in that moment.
That said, if we flip this around and some guy mouths off while you're enjoying yourselves and you don't allow it to affect you and instead correctly realize that some guy acting like a donkey isn't nearly important enough to surrender your happy frame you don't get riled up, and instead you just keep kissing. Now your cutie is going to perceive your calm confidence, she is going to feel less threatened and uncomfortable and gains the benefit of enjoying that happy space with you for longer than she otherwise would (unless you're a really bad kisser

).
What's the difference? Uptight dude experiences less happiness, his cutie experiences less happiness, and she will associate the slew of negative feelings that come up when being taken out of the moment with uptight dude. On the other hand, chill dude experiences more happiness, his cuties experiences more happiness, and she associates the feelings of happiness, security, and so on, with chill dude.
Bottom line: chill my man.