All is pretty much said above but the song is so compelling and frustrating as to origin that there are many, many comments on it.
Several of the more sea-oriented comentators make the point strongly that the ship couldn't in any way have been the famous clipper. They go to lengths since they are deeply insulted that one of the greatest of all sailing ships might be so tainted and slandered. It is stressed that every day of the ship's history is recorded in existing logs from the day it launched till it died. Apparently, not only was there never a pirate ship of this name but no Flying Cloud at all before 1851 back to the early 1600's.

Another interesting aspect is the throw-away comment in Rickaby. In his great early study of Michigan logging songs he (like Doerflinger) records the many examples of sailors working off-season as loggers and bringing the sea songs with them. It was said (he said) that no one could get a job in a logging camp unless he could sing "The Flying Cloud" straight through. Exaggeration as this may be, it shows how popular the song was in North American tradition.

I sing the version from Palmer & I sang it a couple of months back at the local club. One person asked, if the FC actually:

9.The Flying Cloud was a Yankee ship of five hundred tons or more;
She could outsail any clipper ship hailing out of Baltimore.

then how come she got caught by the man-o'-war, the Dungeness?

This showed that a) at least one person was actually listening and b) one needn't take ballads totally literally.