The best way to flirt with someone on Twitter? Two words: Favourite and Retweet!
Favourting and Retweeting a person's tweets is the absolute best way for them to notice you. If it is someone that you do not already know, it's a great way to draw attention to your profile and get them to follow you. So, before you do anything, have a check of your own timeline and make sure it doesn't have Tweets that might put them off!
Be subtle though. Don't just systematically favourite everything they've ever tweeted. Do it to the tweets that genuinely interested you, or made you laugh. And if you have an appropriate comment to add, then reply. We all like to know that people are reading our tweets, so I am sure they will value your input, and it's a great way to lead into general conversation with them.
If you see something that makes you think of them, or of something they have tweeted, give them a mention on your timeline. Again, it's another good "in-road" without just tweeting "hey, what's up?".
As you get talking to them more, you can amp up the flirting if you feel it is appropriate.
The key: don't go for too much too soon, build up a relationship with them gradually, and then maybe take it into a more private setting. Flirting over Twitter is fine, but if it looks like things might be a progressing, I'd suggest at least switching to direct messaging!