Color averaging can be interesting for photos, but there it's a visual effect not a data conveyance.

How about taking the average or top colors of all photos taken in a country and rendering it on the map?

While it's nice to plot colors, to me this is a good example of average being a meaningless statistic for a set of data.

What does the average of a set of colors mean? What does it tell a person?

If you pick random colors per country does it look the same as this map? I'm guessing it does. If so, the data is telling you nothing.

How about plotting the age of the flag for each country as a heatmap?