All learning is by immersion. The best way to start learning flirting is to observe couples on dates, and note their body language. You don't need to be close enough to hear their voices, since body language will be your important leader. If you can hear them speak, even better. You can also make it into a social outing by bringing along a friend and making running commentary on the date (this will help you exchange notes and speed the learning process, and it will also make learning fun and thus increase retention). Note that these things (esp #2) are both fairly socially unacceptable, so be aware of that and try to be somewhat discreet.

Once you do that, go out and use the body language you've learned to indicate flirting and assess other's reactions. Test, adjust, repeat. The hardest part is that you'll need to find a group of people whose opinion you don't care about until you're vaguely OK at it. I suggest parties, not bars or clubs, because they are the most conducive to the wide range of flirting you'll tend to want to master.

When learning just about anything, there's a period during which the rate at which you discover additional aspects about that thing which you don't know is greater than the rate at which you learn. So, your self-assessment of capability decreases before it increases. At least this always happens to me. I've come to accept this as a sign of progress.