My husband ordered what he thought was a traditional Cherokee flute, however it was made of bamboo. So, he does not consider it traditional because it was not made of indigenous wood.
There are a few bamboos native to the United States, they are Arundinaria gigantea also known as river cane, A. appalachiana (hill cane) and A.tecta (switch cane). All are found in the Southeasern parts of the United States. It might be possible to make a flute from River Cane which is indigenous to the Southern Appalachian region from which the Cherokee also come form.