Academic journals aimed at publishing work by high school students
Publishing in early career
If the research is good enough, it will get published. The challenge is to do good-enough research as a sixth-form student. Actually, that's a challenge for any of us, at whatever stage we're at. The best example I know of, of young researchers getting published, is a paper in Biology Letters from a class of 8-10 year olds. The paper, Blackawton Bees, is a good bit of research and an entertaining read.
Principal finding ‘We discovered that bumble-bees can use a combination of colour and spatial relationships in deciding which colour of flower to forage from. We also discovered that science is cool and fun because you get to do stuff that no one has ever done before.
Actually, never mind the rest of this answer for now. If you're reading this, whoever you are, and you haven't read the paper before, just go read it now - it's free to view for all. You'll thank me (so remember to come back here afterwards ;-).
Journals for students
As far as journals specifically for students: well, they all are, really. Pretty much all of us who are reading them, are reading them for study. God knows, they're almost always so dryly written that no one would read them for pleasure.
There are exceptions. For easier reading, there's New Scientist and Scientific American; though the science sometimes suffers in the cause of circulation-friendly journalism, particularly for New Scientist.
More digestible science
And there are quite a lot of science blogs on the web, which make for more digestible reading of recent research. Unfortunately, there's also a much higher number of pseudo-science blogs on the web, that, unless you know a lot about the subject, are hard to distinguish from real science, but contain pure unadulterated nonsense. For example, Real Climate is respectable science by respected scientists; Watts Up With That is unadulterated pseudo-science nonsense; but to the unwary, they are both climate science blogs. So, for finding new science blogs, reader beware. Even well-established science blogs sometimes go off the rails, when they stray outside their area of immediate expertise.
I have never heard of an academic journal specifically meant for high school students. There might be magazines directed towards publishing projects of high school students, but I would not call these academic journals.
In regard to publishing, in principle if you have something that is of sufficient level to be published, you could just submit the paper to any journal. It would then be reviewed. The major hurdle would probably be that you do not work for a reputable institute or university. You could try and remedy this problem by looking for a supervisor who already works at an institute/university who would be willing to collaborate with you.
That said, realistically I do not know many 3rd year university students who have the level to write good and relevant academic papers. So, it might be a little far fetched to write an academic paper in high school. Than again, if you feel that your contribution is worthwhile, please feel free to ignore this advice.
Good luck!
I started one with that goal in mind back in high school (I'm in college now). Although it definitely cannot compare to fully funded, top tier journals, we strive to provide a learning experience. The journal is edited by 2 sets of people, professors and other students. The professors are there to help teach both the author and the student reviewer about the journal process, and provide his or her experience when it comes to publishing and academic work.
You can check it out: The National High School Journal of Science