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It's hard not to agree that Amazon is being flooded with novels. The thing about making it possible for everyone to publish their stories is that it means everyone will do it. Though, that most of it isn't, well, exactly publishable. So if you want to stand out among the crowd, your first job is to write some quality stuff. True, some genres sell more than others, and you might disagree about the quality of the stuff that sells well, but generally more well written stories will have a better chance of succeeding within their genre.
Your second job, as Veritas suggested, is to write more quality stuff. J.K. Rowling didn't get published on pure luck (if that was the case, the first publisher she sent it to would've published it -- which rarely happens for any author, by the way). She got published by writing quality stuff, having a bit of luck, and most of all being persistent. (If you want to know true persistence, try looking up how many times Dune was rejected)
The strategy for making a living as a self-publishing author is pretty clear as well. 99.9% of the authors who make it that way does so by consistently putting out new material, thereby making is possible to live of a smaller group of dedicated fans. Doing some marketing is going to be necessary as well, but that will only come in handy if the people you manage to lure towards your stories will actually love them.
I feel your pain though. I'm actually dreading the day a little when I manage to create publishable material consistently and have to start selling myself.