The Flag Resolution, signed in June 1777, formalized the US flag as being composed of stars and stripes. The Betsy Ross version, with the stars arranged in a circle, came shortly thereafter.
The Treaty of Paris, which formally ended the war, occurred in 1783. The final significant defeat of the British came in 1781.
So there was plenty of time during the war for the flag to be around.
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"It's a magical world, Hobbes ol' buddy...let's go exploring!" - Calvin
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