One million percent /zeen/ (from someone who has been making and trading zines for almost 30 years). Just a few https://bobdoto.computer/ZINES-1

I've never heard anyone say Z-I-N. Zeen.

I've always said zeen, because of magazine.

It's technically pronounced z-ee-n (because it's short for magazine) but lots of people who aren't familiar with the origin and/or learned the word online say z-eye-n and it doesn't do them any harm. Both pronunciations are usually understandable from context.

I always pronounce it as z-eye-n