One way to achieve a matte finish is to use a simple 3M plastic
Scotch pad. Just run it over the wire or chain and it will dull the
finish. It is not really a permanent treatment however and will
gradually shine with use. You can cut out little wheels of it and use
it with your flexshaft as well.
If you want a more permanent matte finish, get an Paasche 'air
eraser' from you local hobby shop where they sell air brush supplies.
Connect it to a small compressor and, using glass balls, aluminum
oxide compound or other mild abrasive, you will achieve a rather long
lasting matte finish....and it will be quite even in texture as well.
Cheers from Don at The Charles Belle Studio in SOFL where simple
elegance IS fine jewelry! @coralnut1