I'm going to get straight to the point. If you want to exit the platonic zone, you need to focus on two things.

Number one, it can be done. And number two, you must make her jealous. If you have any moral hold ups or any mental roadblocks that will prevent you from doing it, then continue to listen to the girl of your dreams yap about some other dude that makes her horny. No self-respecting man should allow such emasculating events to occur, but it happens all the time.
Like I said, it can be done. I've personally been on both side of the equation and I have personally experienced the effectiveness of it. Meaning I have had women that I regarded as not sexy enough to be romantic with, only to have them make me jealous to the point where I ended up sleeping with them or in most cases trying to without any success.
In these cases, the women weren't intentionally trying to make me jealous, but the effectiveness of doing it has nothing to do with whether the person was actively trying to do it or not.

It has everything to do with sexual value. Making someone jealous is one of the quickest ways to establish your sexual value. I can not stress that enough. In the platonic situation, she is use to you showing her some level of romantic attention. Even if she isn't interested in you, she still will be getting some good feelings from the attention you show her. 

Therefore, by showing that your interest in elsewhere (making her jealous), you are cutting off the platonic friend's good feelings. She will lose a happy source. She will be drawn to you on a level that she can't quite explain.  An unconscious attraction will always be more powerful than a conscious attraction.  

For some reason, female friends love to talk about other guys to their male friends like he is one of their girlfriends. Not only is this a fact, it's an indication that you have zero sexual value in the eyes of your female friend.

Here's how to reverse that.

The key is to bring up another female or a past experience with a female with great detail. If you do it the right way, you will feel the momentum switch back your way.

Women want MEN. So remind her that you are a man.

Women always love attention.

If you are listening or passively accepting the emasculating (balls-removing) act of being radiated by her lusting over another guy, then that is no different than giving her advice on how to approach the guy or seduce the guy . In either case you basically have the energy of a female. If you want this female friend, it should offend you when she yaps to you about another guy.

The next time she does it, just remain calm. You don't have to externalize your emotions. You will be more successful if you just calmly let her speak. Then when it feels like it's your turn to talk, you can calmly mention your story. This is the shift and you will experience the beneficial magic. You will notice and feel a slight shift in momentum. If anything is ever going to happen between the two of you, this slight shift must take place. This is the easiest, quickest and most fun way of getting it.

So when it is your turn to talk, just remember to be extremely descriptive - to the point where you can sense that it is making her uncomfortable. She must feel the discomfort. This is where most of the points are scored. If you blurt out your story, cut her off, or show that you are frustrated with her talking about some guy, then you are not accomplishing anything.

The idea is to increase your sexual value. Acting overly emotional will not accomplish that.

The idea is to reclaim your sexual value. And it is universal. This works:

1 . If you are just protecting your balls even with a female you don't even care about. 

2 . If you want to increase your perceived sexual value in the eyes of a female friend you are interested in. 

3 . If you want to increase your perceived sexual value in your relationship (often a current girlfriend or wife may mentioned an ex-boyfriend in an uncomfortable fashion - keep in mind, the energy is the same).

Here's how to be real effective at the golden reversal.
1. Be extremely descriptive in your story. You want your story to run through her head. Remember women love fairy tales, so they often exercise their imagination power by daydreaming and fantasizing. 

2 . Be calm. Let her talk. Let her get it out of her system. Don't over-react by screaming at her to never talk about other guys to you. Just let her talk and be calm. You'll get your turn. 

3. You can use it to send other important messages (for example, you can talk about how a girl you are seeing seems like she can't get enough sex from you. You get the idea.)
You will know if you were successful if:

1 . She accuses you of giving too much information or being too graphic -maybe you went too far, but you still got the job done. 

2 . She appears kind of withdrawn or there is a moment of silence - she is reflecting and absorbing. 

3 . She attacks your story or the girl in some way. It's a defensive mechanism. Keep in mind, the art of making her jealous works and it is very powerful. You can actually make a girl jealous within seconds of meeting her. Statistics have shown that jealous wives tend to be more sexual towards their husbands and will often make an extra attempt to look more beautiful.
Remember, this a just a tool that is very effective in reclaiming or establishing your sexual value. Again if you have any moral hold ups, you will continue to suffer. There is nothing wrong with doing this, because the bottom line is if you have no sexual value women will not want to sleep with you.

You deserve sex.
The power of this technique when applied to the platonic friend is that she will not expect it, so you end up communicating a lot of powerful messages. You can perform the art of jealousy in both directions.

Cultivating jealousy is kind of like strengthening your arms. You got to work the biceps (pull movements) and triceps (push movements). Therefore, the TARGET female has to be jealous of your interest being displayed towards (pushing out) another female as well as being jealous of another female showing interest in you (pulling in).

Keep in mind, the beauty of jealousy is that the events can be perceived or loosely supported and they will be just as effective. I told my girlfriend the other day that I had this weird dream that I had sex with the lady across the street (who is super sexy). It worked like a charm. Afterwards, it appeared as if she resented the woman! As if the woman actually had sex with me. She obsessed over it the whole day. Later on that night she put on an amazing sexual performance.  I remember one time I was working at an old job. I wasn't in a relationship at the time, but my female coworker was. She was talking about her boyfriend and how wonderful he was, so then I started talking about this girl I was seeing.

I didn't necessarily take offense to the talks of her man, but shortly after describing the events with the girl I'm seeing, the co-worker appeared to get jealous - even though she was admittedly in a loving relationship. It was obvious. At the time I wasn't trying to make her jealous, but shortly after we finished talking she scheduled an "appointment" in her book for us to hook-up.

Obviously nothing is guaranteed, but to greatly increase your odds of success you want to make sure that the friend is getting something out you giving her romantic interest in her. For example, if she smiles very hard, after a compliment, then that is an indication of her getting something out of it - even though she may be rejecting you on the romantic level.

As a pre-step you may even want to pump up the flattery for a few days, to get her quite addicted to those feelings. You want to maintain those good feelings she is getting from you over a certain period of time. This will get her really addicted to those good feelings (and addicted to you, because you are the owner of those good feelings). Then you want to cut off those feelings instantly and place them elsewhere. This created a shock. In other words, you want the friend to gain knowledge that you are pursuing someone else. And it is more effective if the friend has the perception that the other female is interested in you.

Once your female friend starts showing interest in you, don't be so quick to run in her arms like a lost puppy does when he's reunited with his owner. There's plenty of resources out there that explain how to keep her interested, but the main thing you want to focus on is being nonchalant.

That should take you pretty far.