What ships make a good flag ship in Sid Meier's Pirates? Is there an advantage to keeping a smaller ship or should I try to use the largest ship I can find?
There's always a tradeoff, so you'll need to tailor your choice to play to your strengths and your usual choice of prey.
Smaller ships have better speed and maneuverability, but they don't have much in the way of cannon space and even with triple hammocks you'll be taking a fairly small boarding crew. You can dance circles around larger ships, but you're going to need to because you'll need to hit them a lot of times to reduce their crew complement before boarding, and they only have to get in one lucky hit to ruin your day.
Larger ships have stronger hulls to take more punishment, bigger crew complements to help you when boarding, and lots of cannon to cripple anything that gets into your range. Downside here is that they tend to be ungainly and anything smaller than you will likely manage to successfully Run Away -- and a ship that escapes means a ship that you're not getting any money from. Likewise, sunk ships can impress the governor, but it doesn't net you anything.
My personal favorite is the Brig of War -- in my opinion, an excellent cross between speed, maneuverability, firepower, and crew complement. Especially when fully upgraded it's fast and quick enough to catch even a sloop unless it's running with the wind from the moment the encounter starts, and enough firepower (and crew complement) to make even a Spanish War Frigate think twice about trying to engage.
Best of all, Captain Kidd sails in one, so it's always possible to encounter at least one of them -- as opposed to the Ship of the Line, which requires seriously annoying non-Spanish factions before it becomes available, and every one of them will be armed to the teeth and gunning for you.
EDIT After giving it some more thought, my main counterargument to the Ship of the Line is that in order to get attacked by one and in order to be able to capture it, you pretty much need to have advanced to the point where nothing else is any kind of threat at all, which limits its utility, whereas the Brig of War can be acquired fairly quickly if you're bold and skilled and will serve you well throughout your entire career of mayhem and plunder...
Your flag ship will always be the one you take into combat so ideally it should be the ship you have that is most suited for that task. Qualities that would make a good flagship are:
My personal favorites for a flag ship is the sloop of war, a frigate , or a ship of the line. An Indian war canoe can also be very deadly in the right hands as it is extremely maneuverable.
I find the Brig class a bit too unwieldy, it's not quite up with the real heavy hitters, yet lacks the maneuverability and speed of the Sloop class.
I usually trade the initial ship up to a Sloop of War quickly by taking a pirate raider, escort ship, or pirate hunter, and once they become available, my preference is a Royal Sloop. With 20 cannons and 125 crew (187 with triple hammocks) you can engage any ship. You don't have to worry about accidentally sinking ships with a particular good first salvo, and often can evade almost all enemy fire.
With two Royal Sloops I also have a switch-off flagship when a battle was a closer shave than I wanted, while being fast on the world map but being able to field almost 400 pirates to attack cities.
Sometimes, when I find Henry Morgan with his Large Frigate or an invasion force with one, I get a Large Frigate or Ship of Line additionally, which with Reefed Sails have a very nice turning point as well, and can carry 40 (SOL 48) cannons, and up 250 (SOL 300) by themselves outgunning even war galleons.