To start off, we can reduce the number of flags to look at with some simple deductions.
The only national flags able to be made on a rubik's cube, would be ones of either 3 horizontal or vertical stripes, with no "extra" pieces (No stars, no crowns, whatever), and can only use the Rubik's cube colours, those being Blue, Yellow, Green, Red, Orange, and White ...
The countries are:
According to the hint, we should use abbreviations of the countries, though. Let's use the top level domains:
There doesn't seem to be a way of making these equations valid sums by converting bases or enumerating letters, but we can turn these abbreviations to numbers by ...
So the flag that should replace the question mark is ...
The translated text:
"Samuel Joseph Alfred":
I don't know how you guys normally do it, but this is how I translated from flags to morse code, since I'm a ruby developer (Not the best code, but it did the job :) ):
Assuming the images were not altered (e.g., compressed) when uploaded, this could be a partial:
Now, if you look closely, you'll find that in the image with the message...
So, when converted we find:
Which could be: