I think to remember, national (or in general?) flags are not allowed on Zippos, except the US flag. Alongside with many other stuff.
The limitations are pretty extreme, and all goes under review, with the risk that you have to wait 1 month just to get a note that you have to deliver proof of your artwork and then wait another month hoping for the best.
After reading their policies, I instantly decided to avoid the hassles. Especially for custom works. It's a shame, because Zippos are great gifts. Used to buy a lot of them as friends' gifts, back in my younger times, and have a nice collection myself.
ETA: Checked the terms and apparently I'm wrong, it's only the Chinese flag that is explicitly red flagged: "Do not use insignia of government agencies, organizations, or military branches, or the Chinese flag." Wondering why I thought, all flags were on the ban list, hmm...
You were right after all! Just got an email, concerning the flags I put on the zippos, indeed only the American flag is allowed - see below!
The details of your product are below:
Product Title: GREEK FLAG
Product Type: Zippo Lighter
Record ID: 5353913
Result: Not Approved
Your design contains an image of a flag that is not permitted on Zippo lighters. Only images of the American flag are permitted on Zippo branded products. For more information about customization guidelines for Zippo lighters, please visit: https://help.zazzle.com/hc/en-us/articles/227351367
I visited the url in the quote above and read it, just like you did, I think. There is nothing in there to be found about national flags, apart from that line about the Chinese flag. I don't quiet understand it, but there is not much I can (or even want) to do about it.
the Chinese flag that is explicitly red flagged
Well, the Chinese flag IS red...