I suppose you could use an old silver pillbox? If you peruse around some antique shops or eBay I’m sure you can find a pretty nice one for not too much money.
I haven’t seen a metal one associated with a flute, let alone clearly originally associated. I love the little turned cocus ones that were certainly original accoutrements. I was lucky enough to be given a “spare” one that had lost its own flute/case etc. by the late Paul Davis as a thankyou for taking a client to him - a friend who bought a flute. My R&R (acquired from Paul) had lost all of its own original kit, but now lives in a lovely (if battered) C19th mahogany veneer flute case that had lost its flute, with Paul’s grease pot.
I have an old, first year of manufacture, 1915, silver flute, which was/is in fine condition, complete with original case, but it was missing its cleaning rod. I then brought the flute back to its manufacturer, W.S.Haynes, of Boston, and no less than the then, but now late, president of the company, Lewis DeVeau (I hope I got the spelling right) gave me, free of charge, the very rod that was missing, complete with screwdriver built into the non-swab end.
I personally find this rule ridiculus. I don’t see any of those posts as being commercial in nature. Also I don’t see why you can’t post a picture of the pot. You don’t sell them, right? Mebbe if some of us are interested you can PM a photo to us?