This question apparently has been answered previously by /u/davidAOP which can be found here: https://redd.it/26884j

The pertinent portion of post is:

Now for the parrots - again, Treasure Island is responsible. In the realm of influencing our modern perceptions of pirates (that isn't also technically a period source, that award would go straight to Charles Johnson's General History of Pyrates, 2-volume worked published from 1724-1728), there is almost a tie between Stevenson's book, Howard Pyle's art in the late 19th and early 20th century, and Disney from 1950 on. In Treasure Island, Long John Silver has a parrot called Captain Flint that says "Pieces of Eight". Before that, pirates didn't have any particular stereotype for parrots - just like they didn't have any particular stereotype for wooden/missing legs, hooks for hands, or eye patches. Sailors of the Age of Sail were known to occasionally acquire animals in foreign ports through purchase or trade. Some may have kept them as pets for themselves, but at least with the case of parrots, they were also excellent profit to sell back in non-tropical ports (especially Europe).

Additionally, this question and some similar to it can be found in the depths of the /r/AskHistorians FAQs which can be found here: https://www.reddit.com/r/AskHistorians/wiki/dailylife#wiki_piracy

Thank you to the people who linked my comments and the FAQ I set up for pirate history stuff on /r/askhistorians. I'm still kind of surprised that this frequently asked question got so much attention again. So, I guess I can try and at least add some additional reading references for those interested in the development of the historical pirate stereotype in popular culture.
The development of the pirate in popular culture and media has recently received notable attention in academic publications. If you are interested, please read the following texts:

Treasure Neverland: Real and Imaginary Pirates by Neil Rennie (2013)

British Pirates in Print and Performance by M. Powell (2015)

Pirates and Mutineers of the Nineteenth Century: Swashbucklers and Swindlers by Grace Moore (2011)

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