Note:
Not my work. I found a thread discussing this on reddit, and thought I'd share it here.
Link to original comment here.
In 1810, rather than accepting China's offer of amnesty, Ching Shih orders her fleet deep into the Pacific. Stocked with months of supplies, they intend to establishes bases among several islands and continue raids, now against ships engaged in the increasingly valuable New World to Asia trade routes. Ching Shih, following stories of Captain Cook's misadventures in Hawaii, goes to the islands.
Upon arrival, Ching Shih negotiates with the Hawaiians for a secure port. Many are sick from smallpox brought by the English. China's deeper knowledge of disease theory, especially
innoculation, leads Ching Shih to promise medicine in exchange for some land. She also offers weapons and metal to the currently destabilized Hawaiian kingdom. Kamehameha the Great accepts and gains a large fleet commanded by Ching Shih, with hundreds of ships and tens of thousands of pirates.
The partnership flourishes fast. Ching Shih's pirate code and Hawaii's own legal system blend and govern the new relationship. The pirate fleet continues its raids, but transforms swiftly into something resembling a proper navy. The Hawaiian Fleet patrols large swaths of the Pacific, collecting "tolls" from all ships it finds, and "taxes" from many of the surrounding islands.
Many of Ching Shih's captains take husbands and wives from among the Hawaiians. Their adventurers attract many young people to join, especially women, who are drawn to the egalitarian fleet and the promise of wealth. Ching Shih and Kamehameha work together to promote ambitious Hawaiian men and women to the rank of captain, which creates a strong, motivated, and loyal fleet to serve the Islands.
In 1814, Kamehameha and Ching Shih begin a public relationship. They produce no children, but the relationship enhances the legitimacy of the fleet and ensures their loyalty to the royal family. Queen Kaʻahumanu fears loss of influence and begins maneuvering against Ching Shih. This prompts a months-long political scuffle, which ultimately leads to the King declaring that a council of captains will decide inheritance of the throne upon his death by electing one of his own family.
After his death in 1819, political powers effectively transfers to the fleet itself. They elect Kamehameha II, who inherited the throne in OTL, but in this ATL, rather than being a figurehead for the Queen, he is a more active leader with the respect of the fleet, having already served on some of its ships.
Kamehameha II leads for 10 years - his adventures in the Pacific stop him from visiting Great Britain, so he does not die of measles. Instead, he dies in a great storm in 1829. His decade of popular rule cements the Fleet Election system.
Ching Shih remains very influential after 1829 but largely retires. She sets a precedent that captains should not accumulate too much political power by turning down many official positions and offers of land. She also eschews new offers of marriage. She settles into the role of elder stateswoman.
In 1830, the Pirate Kingdom of Hawaii is recognized by the USA. American merchants had been dealing with them for a few years, accepting the taxes they must pay to travel the Pacific, since payment guarantees safe passage as well as protection from much worse pirate attacks. President Jackson decides to recognize Hawaii formally to thwart Britain in the Pacific, and also hopes that Hawaii will be a platform for greater trade with China and Japan. Martin Van Buren sails to Hawaii to sign the treaty with the PKH.