From the US Customs and Border Patrol website
Is bamboo allowed to be imported to the US?
In general, bamboo that is not thoroughly dried and is therefore still capable of propagation is prohibited entry into the United States.
Bamboo that is thoroughly dried and split or cut lengthwise (rendering it incapable of propagation) will be inspected upon entry and released.
Unsplit dried bamboo canes/stakes/poles also are allowed entry into the United States after inspection: however, if the bamboo canes/stakes/poles are intended for garden or nursery use, the shipment must be fumigated (T404-d treatment extended to 24 hours) upon arrival at the U.S. port of entry.
Bamboo furniture, bamboo cloth, and other manufactured products made of bamboo do not require fumigation and will be released upon inspection.
His flutes were cut, dried, and incapable of propagation. The border patrol agent was clearly in the wrong.