Official insignia for regions?

Solution 1:

There are no official insignias, flags, or logos for each region. The closest representation I was able to find was either the badge collections for each region, or map artwork. There are lots of other options for things you can do to uniquely represent each region, however, including referring to them by name, by their Kanji, or by League Trophies (though Hoenn and Sinoh are very similar, and Kalos doesn't have one yet). There are also a number of different fan created variations on what flags might look like all over the web, including some inspired by the real life regions the maps are from, which may work as well.