Native artists, that perform with the flute, that I've been listening to recently:
R. Carlos Nakai, Kevin Locke, John Rainer, Jr., Johnny Whitehorse (Robert Mirabal), Hovia Edwards, Gentle Thunder, Kieth Bear...
Other's who perform on Native American Flute:
Coyote Oldman, Autumn's Child (Mark Holland), Scott August, Jeff Ball, Randy Granger...
Some are more world flute performers that also play Native American Flute:
Gary Stroutsos, Peter Phippen, Cornell Kinderknecht,...
More come to mind that are typically found in the New Age section...
Douglas Spotted Eagle, John Huling, Ah*Nee*Mah (David Arkenstone), Golana,...
Of course this covers a wide variety of styles, from simple solo flute to new age orchestration to jazz to flute led bands.