Using SVG from Wikipedia to fill polygon?

In InkScape, try saving the image as "Plain SVG" if you're not already doing so. Also try positioning the center of the flag in the upper left corner of the canvas (this is origo of an SVG.)

You have to create a folder called "svg" in your ".qgis2" directory. You should be able to find this in:

C:\Users\(your user name)\.qgis2

Then create the new svg folder, insert your flags in there and you should be able to see them in your Style > Symbol interface:

For me, QGIS did tend to run a bit slow so it may be a good idea to first follow the answer provided by @hexamon.

I made a tutorial to show how I did it.