This depends on a lot: age, culture, gender, etc. That being said, I do have some generic advice to give.
Eye Contact. Eye contact is a really major part of flirting. First, it establishes that you see and acknowledge the person. Beyond that, if they maintain eye contact, it can indicate mutual interest. It is also a general part of open body language, which is really important (and my next point).
Open body language. Shoulders open, chest forward, arms not crossed, back straight. Someone who is slouching or has their arms crossed often looks closed up, and while in some cases that may come across as cool, it doesn’t come across as approachable, which is essentially the point of flirting.
Smiling. Again, your character wants to look approachable. Smiling is a really easy way to do that. It is also a good way to show that the attention is positive, as opposed to staring at someone because they have food in their teeth, are doing something that they should stop doing, etc.
Physical contact. If your character is close to someone that they’re flirting with, they should touch them. It doesn’t have to (and shouldn’t) be aggressive grabbing or patting, but instead touching a shoulder, arm, hand, or knee. They should also position themselves close to someone that they’re flirting with even when they’re not touching.
Teasing. This is a really common verbal way of flirting, though one needs to be done carefully to make sure it’s not mean, because it can cross that line. If the character does cross that line accidentally, or hits a nerve that they don’t know about, have them cover it up with some more flirting, something that would keep the person’s attention and make them not be angry anymore.
Funny stories. Telling a funny story is another good way of flirting, because laughter can get people to open up. The conversation would probably need to be more than just funny stories, but it can be a good way for your character to get someone to open up.
Be suggestive. Again, something that a character would need to be careful of (and fairly confident to do). This can also be done over text, messaging, etc. so it can be a long-term way of flirting.
Awareness of others. A flirty character should be aware of the people that they’re flirting with. That isn’t just knowing that they exist or physically where they are, but what their responses and body language are. Unless you want them to be a mean or harassing flirt, they should be aware of when the person is sending the sign that they want them to continue and when the person is trying to get them to leave them alone. If it’s the latter, they should probably leave them alone, because otherwise they just come across as being obnoxious and/or a bad person.
Accentuate their chest and/or butt. For the chest especially, a small chest can be disguised depending on the clothing, and so a flirty girl with a small chest would probably wear clothing that disguised it, while a flirty girl with a larger chest would probably wear clothing that showed more of it off. Necklaces are also useful, because playing with them can draw the eye to the chest.
Make sure the character doesn’t come across as creepy/too aggressive. I have read more stories than I’d like where a guy’s “flirting” comes across as creepily sexually aggressive, especially when he doesn’t know the girl. This tends to happen significantly less with girls flirting, but when men are written as being suggestive, it tends to be essentially “here are all of the ways I am planning to have sex with you” instead of “oh, I’m not dressed because I just got out of the shower ;)”. The latter can be flirty-suggestive. The former usually reads as stalker-rapist-creepy.
Think about why the character is flirting. For some people, it is because they just like to flirt. For some, it might be because they’re looking for sex. For some, it might be because they’re looking for a relationship. For some, it might be because they like the power it gives them. The way they flirt should depend on their reason for doing so.