Here's version 1 of my map of flagships currently in POTCO. Lines show where they start from, circles show where they usually stop to roll in circles.
The EITC Corvette, for example, can usually be found at Outcast island on any quiet server. Once you sink it, race to Kingshead to pick up another (if stuck on the fine cutlass quest.)
The Navy Greyhound and Navy Bulwark (that used to circle Devil's Anvil) were taken out of the game when they were trying to fix the "take over another ship" glitch, but mysteriously were never added back in once corrected.
The six French and Spanish ships sail mainly in tight circles (the blood scourges go back and forth a bit more than just a circle.)
You'll notice the various flag ships return to their starting points after a few minutes and circle there instead. After a few more minutes, they repeat their original course again. (Different flagships have different time thresholds.)