If you are looking for a sample of some of the earliest recorded "modern" Native American Flute music, I highly recommend this recording by Doc Tate Nevaquaya. I purchased a copy of the record on eBay a few years ago and I love it. But it's not digital and so I can put it in my iPod. However, you can purchase a CD from Smithsonian Folkways recordings. This album was recorded in 1977 and the best part (I think) is the introductions which Doc Tate does for each track. He tells a story about the song or learning to play the flute and then plays the song.
His style is unlike anything which you will hear in today's recording/performing Native American Flute artists, but it's like stepping back into the past and hearing what the original songs must have been stylized like.