Hi Justin,
I was wondering if you are playing shakuhachi or one of the various sideblown flutes...
I have recorded shakuhachi many times... concerts and my own practice.
The Sony recorder is probably fine, you might like the Fostex FR-2LE as it accepts XLR microphone cables, a better choice than the stereo mini-plug of the Sony. What I hear is that the built-in microphones on the Sony are decent, but your flexibility for positioning is rather limited.
With the Sony, your mic position will pretty much have to be facing you (and your duet partner) equidistant. You can vary how far the recorder is from both of you to get more or less of the room ambiance (greater distance == more room, closer == less of the room sound). This sort of X-Y positioning is actually very good for acoustic streo reproduction, so it's a limitation, but not that serious.
I seem to recall the Sony (with mics) costs about the same as the Fostex, but then you need to purchase microphones. If you want to go that route, you will also need mic stands and cables, just things to consider. But if you go that route you will have a lot more microphone positioning flexibility. You could, if you wanted, position a microphone fairly close to each of you as you play. (Two close-up mics are probably a worse choice than X-Y!)
If you want to also pick out microphones, I recommend starting out with something not that expensive. A pair of relatively inexpensive mics like the Shure SM-57 or 58 positioned well can make a better sounding recording than something expensive positioned poorly. Your first recording sessions _will_ be a learning experience! Even though it's a flute, Shakuhachi does not have a huge frequency range. Don't feel like you must have microphones that are flat 20-20,000 Hz. The biggest problem with those Shure mics is the low output of the dynamic mechanism.
Generally you will find that closer microphones give you a more analytical, dry, clinical sound. Too close and you get breath and finger sound. As the microphones move farther than the players, you get more of the room sound which can be either good or bad depending on your room.
For What It's Worth (not that much, really) I mostly use Audio-Technica AE5100 or Beyerdynamic M-88TG microphones. The AT mics work better with my recorder, but I like the M88s for a dynamic mic.
have fun!
-mike