It also needs to be pointed out that in the original posting the capstan is being used to raise a cable (which is reported as being flaked) meaning the anchor cable. Depending on when this song was coined, this could have been a fat hemp cable, or a chain, the word having being carried over when chain technology got good enough to be used for anchors.

I have heard flaked being applied to chain and to sail, but I have always thought "faked" was correct for towing lines, mooring lines and other ropes -- this could just be an opinion on my part.

The American heritage dictionary provides the following for "flake":

flake 2 (flEk) n. 1. A frame or platform for drying fish or produce. 2. A scaffold lowered over the side of a ship to support workers or caulkers. [ Middle English fleke from Old Norse fleki hurdle]

and only provides the rope-handling definition for "fake":

fake 2 (fEk) n. 1. One loop or winding of a coiled rope or cable. v. tr. faked fak•ing fakes 1. To coil (a rope or cable). [ Middle English faken to coil a rope]

Note that the use of fake to coil rope goer back to the Middle English era, while the root or parentage for flake is totally different.

Regards,

A.