Make no mistake, flirting is a skill, an art form, that some people are naturally good at and others, like myself, have had to work at. If flirting is not your forte, then like any other skill, the only way for you to improve is with practice.
I know we have been conditioned to not talk to strangers. Stranger danger! However, in order to get comfortable with flirting, you are going to need to overcome that conditioning. See the easiest people to flirt with are, in fact, strangers. The key being that they are a stranger you have no real intention of pursing.
Before you flirt with that guy or girl whose mere presence makes your pulse speed up, you want to get comfortable with the idea of flirting. You want to be able to approach someone confidently, without seeming overly eager or creepy. This is where flirting with an attractive stranger you have no desire to actually date comes in.
The beauty in flirting with a strangers lies within the anonymity of it all. This random person will most likely never see you again, so if you make a fool out of yourself, you never have to face them a second time and deal with your shame. Sure, they’re going to tell their friends about you, maybe even tweet about you, but they don’t know who you are, you’re just a stranger. Meanwhile, you can lick your embarrassed wounds and move on.
Flirting with strangers is going to ease your ability when it comes to approaching people. Not only will you will learn what works for you, you will also learn how to deal with a brush off. Sure, it will sting a little, but the blow your ego takes will be minuscule since you are not in this for the experience and not for the potential relationship. So, if they do not flirt back, it does not matter.
This is not an attempt to pick someone up or to get them to spend some monetary amount on you. It is not a moment to take advantage of someone’s good nature. Think of it instead a giving a random stranger a genuine compliment with no intention to take that compliment any further.
For example, you’re in the grocery store and you spot someone who you find attractive. Now is your opportunity to initiate some harmless flirting and break the ice. Go up to them and ask them where they got something in their basket/trolley. Once they point you in the direction of said item you say something along the lines of, “Helpful and attractive! Thank you.” And then – now, this is the important part – you leave.
You do not want to hang around and prolong any conversation, or come across as overly flirtatious, nor are you interested in exchanging any type of contact information with them. You have done what you intended which was to pay them a simple compliment and go about your business. They feel happy to have a stranger pay them an honest compliment with no expectations attached to it, and you have just seen that starting up a conversation with someone actually can be just that easy.
Once you feel comfortable flirting with strangers it is time to upgrade to flirting with semi strangers, people who you are acquainted with and see on a regular basis. That barista at the coffee shop you go to every morning, the post guy that delivers your packages, someone who takes a class with you at the gym once a week. These are people who have seen your face enough to know who you are and you will see them again. Flirting with them gives you some level of accountability. Here, if you do make yourself look ridiculous in one way or another, there is no hiding from it. While that will be embarrassing, it will actually help when dealing with the rejection of someone you are genuinely interested in seeking some sort of romantic relationship with. Think about it, if you can face a person you’ve made a fool out of yourself in front of and survive, then making a fool out of yourself in the presence of a potential love interest who you will never see again, while still embarrassing, is less cringe worthy.
Once you are comfortable in these two arenas then flirting with someone you want to exchange phone numbers and saliva with will become less intimidating. You would have seen that rejection is not an embarrassing abyss from which you shall never emerge, and you will have discovered your own flirting style/technique with which you are comfortable and confident. 
