The flags were made a while ago when there was less than 11, we will have to add a few more in the coming days.

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:

https://oxjs.org/#doc/Ox.COUNTRIES

https://oxjs.org/#examples/countries/live

(The latter has a menu to show more than just current sovereign countries.)

Edited to add: In https://trac.oxjs.org/browser/oxjs/tools/geo you'll find the python toolchain to automatically generate the flag images.