Thanks for making these, but I wish you would have also acknowledged the sources in your LICENSE.txt.
As for the license itself -- even though I used to work on licensing and UI for Wikimedia Commons, I acknowledge this can be quite confusing, so I sympathize. I've rewritten this comment a couple of times already.
It's not clear to me if you can re-release everything under any single license. It's also unclear to me if you can assert copyright over the whole thing, as you must if you are going to use a CC license or the BSD-style license you used.
However, I would suggest that whatever you are doing, you should not arbitrarily reassign the work to a BSD license. They are not designed for graphics, since they require publication of the license wherever the graphic is used. Imagine if you wanted to use the icon on a postcard; according to the license you'd have to include the license text on the postcard. If you want these to be used widely Creative Commons Zero is much better... assuming you can assert copyright for the whole thing as a derivative work.
The really pedantically correct thing would be to list the licenses for each and every flag, but I acknowledge that would be no fun at all, and as far as I know Wikimedia Commons doesn't have tools to make that easy with large collections.
Sorry for the legalese - I think you did a great thing here, I'm just trying to help you share it with others.
Wikipedia took over the world while nobody was noticing. Didn't you get the memo?
You are a bit confused here, but I don't blame you. Here is the legal situation as far as I understand it (IANAL, standard disclaimers apply).
The Wikimedia Foundation hosts content on its servers provided by the community. Usually, the individual contributors own the copyright to all the content. And when they submit content to a WMF site, like Wikipedia, they explicitly agree to license the work under terms such that others can use it. (I am ignoring the case of fair use for now).
Certain kinds of contributions, however, are not original to the contributor. This gets confusing because then you have to prove that it's okay to reuse.
Depictions of national flags are often ineligible for copyright, or are explicitly granted to the public domain, in their country of origin. However, "public domain" has no legal meaning internationally.
The CC0 license is really designed for creators who want to dedicate their work to be freely copied, like public domain, but want something that is legally meaningful.
But - there was a large collection of flags licensed CC0 which became the basis of the Wikimedia Commons collection. Other flags have specific justifications for why they are public domain, sometimes quoting laws from specific countries. This is the good thing about Wikimedia Commons, it doesn't force you into any straightjacket to explain how the license works. But that also means that everything's kind of a mess if you want to get a straight answer to a question like "under what license could I republish all the flags on Wikimedia Commons?"
And that's where it sits. If you squint, everything's not so bad. But maybe Wikimedia Commons should relicense all the flags as ineligible for copyright -- it would make things a lot simpler.
Of course, because copyright is taking over the world, I would not be surprised if there are some nations that would insist they do hold the copyright to their flags. For instance, the EC insists it holds the copyright to their flag and the Euro symbol. Maaaaadness.
For a good list of countries, mostly derived from wikipedia as well, that comes with properties like dependency, disputed, and so on, includes historical data, back to 1970, and whose main purpose, similarly, is a set of flag icons, see OxJS:
