Contrasting pieces

[MeLizzard]

Do you mean Handel sonatas? We have only one Hindemtih sonata, but he wrote one for almost every other instrument, too. A movement from a Handel sonata would be a good choice. Maybe the second (fast) movement of either the G major or F major. If you're not currently taking lessons, I would stay away from using such substantial repertoire as Hindemith and Syrinx as audition pieces. They're too easy for the listener to tear apart if they aren't played at a high level, in terms of technique and expression, as well as performance practice and musical scholarship. Handel is good basic repertoire, though don't consider it "easy". If you're considering studying music in college, these are pieces with which you should become familiar.
Grade levels for repertoire are highly subjective. Many states have their own lists, but often the lists aren't comparable or compatible. If you'd like a relatively comprehensive literature guide, visit the National Flute Association website, and purchase the repertoire guide prepared by the pedagogy committee. I think it's $3. Maybe $5. It's very well organized, down to a chart indicating which skills are encompassed in literature of specific levels. According to their list, a reasonably good high school player is playing pieces from level F to Level I or J. Some literature is purposely excluded; they left out pieces they consider to be beyond the private lesson curriculum for most high school students. You know, there are some things that should just be saved for college!
It'll be obvious to the listener if you're consciously trying to avoid technique, and technical prowess is an important part of good flute playing. Some flute parts in outstanding wind works are every bit as difficult as orchstral exceprts. Some of them are technically much harder than many orchestra parts I've played. So choose a piece with a little technique in it, like a Handel movement, that's stilll accessible and which will flatter your current skill level (make you sound good!).
Can the contrasting pieces be by the same composer? Many times, it's acceptable to play a slow and fast movement by the same composer, or even from the same piece, for auditions. A book to check out is 24 Short Contest Pieces (Southern Music). It contains pieces of many styles, at a comfortable intermediate level, and is a good companion to the book of Handel sonatas. Check out (in this book) the Sicilienne, by Faure, from Peleas and Melisande. This is an early 20th-century piece transcribed from an orchestral work, but is commonly played by young flutists. It's in 6-8 and has long, flowing phrases. I was somewhat taken aback when my husband, upon hearing one of my students preparing it, asked, "Why is she playing a 'cello piece?". I guess lots of other instruments like to play it, too.

[ick27]

If the audition is soon, pick something that you've already played well in the past. Don't plan to play a new work for the first time in an audition. The audition panel will pick the candidates that play flute the best, not the ones that choose the most interesting or diverse pieces. It would be better to play an etude that you know you can play really well rather than to attempt a new and challenging piece.

If you have a lot of time to prepare for the audition, then you do have more choices of what to pick from. MeLizzard's suggestions on this are all very good.

[MeLizzard]

Maybe I should have used the word "critique". Negatively critique. There are always acceptable parameters for performing pieces from each stylistic period, and a private instructor can help with this. The period during which each composition is written influences the style of writing for the instrument (based on the capabilities of the instrument at the time), and our interpretation, including tone color, vibrato use, accurate tempos, ornamentation, rubato (or none), and other elements. While our interpretations should ultimately be our own, there are some rules and standards, and characteristics a critical listener will expect to hear. Syrinx is rhythmically straightforward, but needs strict tempo--not like a cadenza!--plus sophisticated phrasing, extreme dynamics (especially many incarnations of soft), and color variation.
The Sicilienne is rather simle and straight in its demands. Maybe count the rhythm in a quick 6 instead of in 2. Place the occassional 16ths very precisely, with clear articulation. Strive for long, fluid phrases with dynamic contrast and some color diversity. Listen for even, matched tone color throughout all registers, lowest notes to highest. Be sure to change mood a little with the key change.
Choose repertoire for your audition with which you're completely comfortable. You didn't give a timeline, but there may not be time to adequately prepare a new piece. Whether certain pieces will get you into a particular ensemble is terribly subjective. The audition for my first high school's top wind ensemble was two challenging Andersen etudes. After my family moved, I'm pretty sure I was one of two or three students in the new school's whole 200-member band who could play anything that hard!