I'm not sure whether there was ever an actual pirate group that was exactly like that, but it seems like a conglomeration of different.

The large pirate flee run by a family dynasty of pirates could refer to Zheng Yi and Zheng Shi's pirate fleet, which had 300 ships. Zheng Yi was a pirate during the Qing dynasty who was descended from a long line of successful pirates. Zheng Shi was his wife, who took over leadership of the fleet after her husband died. https://en.wikipedia.org/wiki/Ching_Shih

The Pirates on Formosa is probably a reference to Zheng Chenggong aka Koxinga, a loyalist Ming admiral who attacked Qing forces from his base in Taiwan.