I don’t know if this has been mentioned before, but since it’s a pretty easy solution for all those skin irritation problems some of us encounter when playing wooden flutes, I thought I could mention it here:
Get some sort of cellular phone display protection foil, on eBay for example. Cut it to a shape that suits your needs and attach it to the flute. It’s cheap, easy to do, looks good when executed carefully, and it works. It’s even removable without any residues in case you don’t like it.