It would be better if you had a small vibratory tumbler, but lacking
that I’d use any of the medium ceramic abrasives. All of the tumbler
suppliers have some variety of it. The ceramics are heavier than the
plastic ones. Just run your chain in the abrasive - 6 to 8 hours in a
vibe and 18 to 20 in a rotary - checking periodically to make sure
you have sufficient liquid. At the end of the process, you will have
smooth lovely matte finish on your chains. There is no need to run
steel first unless you need to work harden the chain.
If you are running several chains, I’d really suggest getting a
vibratory tumbler, because the rotary ones tend to tangle chains.
And here’s the pitch - there is a book on this subject “Tumble
Finishing for Handmade Jewelry” available from all the major
suppliers - Gesswein, Rio, Otto Frei and others. Get a copy and your
life will be simpler because the stuff about mass finishing is pretty
well documented in it. It gives you product names, times, media
recommendations, a cookbook for times based on metal, finish needed,
etc. I’m biased, I wrote it.