The moment I saw 国 it looked like 
(Japanese flag) and country made intuitive sense. Anyone else see it that way? Is there any historical reality to that or just coincidence?
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I mean it is a 玉 (ball) in a square. So I get it.
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What direction are you suggesting the influence went?
That they looked at the 国 kanji and used that as the basis for the flag?
Just going by the dates, the flag first appeared back when the old version of 國 still would have been in regular use. So 国, even if it did exist as a simplification some people would have been familiar with, I’m not sure it would have been the most immediate thing people would think of for country.
The flag is called 日章旗 or 日の丸, so if it did take inspiration from 玉, it doesn’t seem to reflect it in the naming.
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Influence could have gone either way not sure but it’s one of the better mnemonics I’ve seen even if it’s just coincidence.
Hey I’m at that point too! And now I’ve got an extra way of remembering this one.
Thanks! 
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Ya I’ve found all the kanji with boxes around them intuitive so far.
回 = 
(rotate)
国 = (country)
図 = 
(diagram)
囚 = prisoner
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