The top character is "zhong1", or "middle". "China" in Chinese is "zhong1 guo2", or "Middle Country" (often "Middle Kingdom").
The bottom character is "mei3", or "beauty". The US is "mei3 guo2", or "Beautiful Country", but it's actually mostly because "mei3" sounds like the "mer" in "America".
So the two characters are basically saying China America, suggesting a harmonious union of the two, or something like that, which makes sense given the American flag.
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