"Wappen," I believe, is German for "heraldic symbol," or "coat of arms." So the name of the ship might be translated "Emblem of Hamburg," or something of that nature. Hamburg was one of the states of the Holy Roman Empire that eventually became Germany. I don't know anything about pre-unification German flags, but I suspect that white castle on the red background is the state flag of Hamburg. I have no idea what the flag with the phoenix on it might be.
There seems to be some doubt about the history of La Flore (and even whether she actually existed). I gather she was commissioned right around the time of the French Revolution. The French national ensign during the reign of Louis XVI was, I believe, a simple white banner (white being the color of the Bourbons). I have the impression that pre-Revolutionary French warships sometimes flew white flags ornamented one way or another with gold fleur de lis, but I'm not aware of any consistent rule about that. (Michel - can you help with this one?) After the French Revolution, of course, a French warship would fly the red, white and blue "tricoleur" that's still the French national ensign.
I've got a book about the history of naval flags; I'll take a look at it and see if it contains anything else that would help. But I think the above is the straight scoop.
Youth, talent, hard work, and enthusiasm are no match for old age and treachery.