This may not be an idea to everyone’s taste, but in theory could you make a flute out of this ? The plastics aren’t given their chemical name but I think they’re methyl methacrylate.
http://www.arizonasilhouette.com/Pen_Blank_Images_4.htm
Depending on getting a rod of it big enough?
Anyone want to make one for me? You’d never have to own up… 
If it can be turned into pens, then in all liklihood it could be made into a decent, although perhaps not great, flute. I’m guessing that finding rod stock of that stuff in sufficient diameter may be difficult though. Could be wrong about that though.
Loren
I think these plastics are for extrusion they come in granules in an astonishing number of colours and metallics. The swirly effects are made by mixing in the extruder I would guess.
Celuloid presented a serious problem for me as a kid. Most of our toy cars and things were made of celuloid and when I got too close or touched my mouth to them it stung and left tiny welts on my lips and tongue. Don’t ask me why I was putting the cars there but I did. I could not imagine putting my lips to a Celuloid flute. Alergic reactions are dreadful for flute players. Ask, I think, Loren about that. (was it you Loren?)
BillG
Thanks for your input guys,
Treeshark, do you happen to know a supplier for the granules please? I’ll search the net too.
Loren, do you think it’s very different from Acetal?
And Bill, thanks for the Caveat, I suspect the old Celuloid had a different formula - didn’t it used to be very flammable if not explosive! and I 'm hoping that, because a pen has such lengthy contact with the skin and gets sucked on and chewed as well , the H&S standards of this plastic are better than in the past! I have a pen blank or 2 here, I might snuggle up to the material & see if I’m allergic before I start ordering it in flute lengths…
Any tasteful suggestions for colour? How about the palest blue with faux tortoiseshell rings? White marble with faux ebony rings? Or taste be darned and go for the purple glitter 
Okay, now you all think I’m a British drag queen.
had a look at the blank pictures and I think this would be lovely for a flute…at least I would find it fun to own one…
so please let us know how you are doing!! you never know what you are getting yourself into 
greetings
berti
Hi Julia, I’ve used Begg and Co in the dim distant past. I think they have extrusion facilities as well, though their minimum order might be quite high.
http://www.beggandco.com/
Thermo plastics can be hard to machine, either they are too soft as in abs or splintery as I suspect your pen samples would be. Of course there is nothing to stop you injection moulding the flute parts as many recorders and whistles are made, but the tooling costs can be high though nowadays with cnc cutting they must be less than when I had such things done. Mind you once your Pratten perfected injection moulds were made you could knock 'em out by the thousand.
As for colours, well St Flatley demands it should be glittery with a full bossanova backing…