I only wish I had the command of a clipping privateer to be-gin with and could carry off the Chancellor and keep him on short allowance until he gave judgment in our cause. He’d find himself growing thin, if he didn’t look sharp!’
Strictly speaking, it isn't a type of ship—any ship can be a privateer just as any ship can be a pirate ship or belong to a navy. A ship becomes a privateer because its captain (or sometimes its owner, or sometimes, it seems, the ship itself) has a "letter or marque" issued by one country permitting it to lawfully attack the ships of another, specified, country. A privateer is essentially a private warship, or a licensed pirate, depending on how favourably you view its activities.
Bleak House is set sometime in the late 1820s up to about 1830, depending on which scholar you believe - during Dickens's youth, at least 20 years before he wrote it. Privateers in the sense that Uncle Jack describes them (correctly, by the way) existed at least through the time of the American Civil War in the early 1860s. So, no time conflict there.Thanks, Uncle Jack. To save explaining, I just linked to the dictionary. I wonder whether the "pirate ship" definition still held in Dickens' time?