It depends all on your playing ability and how much you're willing to work on it.
There's Reinecke, which is pretty and romantic. I think advanced high schoolers can definitely play this piece. I think this concerto is a very good option.
There's Nielsen...which is not something every advanced HS can bust. Very difficult. It will absolutely take more than a month to get this piece down (IMO). Same with Ibert. Ibert really shows off the technical chops. The 1st movement just starts out with a BANG. Both concertos are extremely impressive, but very very very hard. If you have the chops, DO it. When you pull it off, it's like murder...and if you don't have chops, it will be very obvious, and the results won't be good...
Then you have that good ol classical Mozart concerto G or in D. Ehh. Within the grasp of advanced high schoolers, most definitely, but it takes a lot of polishing. Mozart is see-through alright. I don't really find Mozart to be a favorite with concerto competitions (unless it's impressive, interesting, and very very very well played), although it is a standard in auditions.
But then again, is it allowed to repeat Poem? Poem is a wonderful, interesting piece. I always find revisiting pieces a good idea. You can realllly polish it, and totally have it in your grasp. It has the potential to bloom and become much much more than it was.
Martin Ballade, too. Hard piece. It is pretty modern, but impressive. I find it a very dark and exciting piece. Counting is a bit of a challenge, and you need some good triple tonguing to pull off the piece.
Chaminade's Concertino. Ugh. Not a good idea for a standard audition. But could be in a concerto competition! Definitely something to pull off if you have your scales down very well. It'll take some time to truly polish the piece and make it your own...but it's certainly easier than Martin or Nielsen/Ibert. I've seen some kids win with this concertino, but it all depends on the kind of competition. If it's a competition with a major, professional orchestra (which I doubt, based on previous concerto winners you mentioned), Chaminade is not really a good idea (nor would be Mozart, imo).
Then there's Liebermann...and Jolivet...yeahhhhh. They're tough alright

I'm not sure what kind of concerto competition it is, but if it is a HS one, don't even bother. Well unless you are a machine.

Now that would be something. /raiseseyebrow
As for Otaka, I've heard one performance of it...by Mina Kitamura I think? It was fantastic, but I think I would go for the standard flute concertos. This is just my opinion.
Here's a good link with standard flute repertoire, the starred pieces are good for concerto competitions.
http://www.webpages.uidaho.edu/~leonard ... edrep.html