I was reading through Quest for Blackbeard: The True Story of Edward Thache and His World and on page 80, one passage read:
As if emulating the destruction of the nearby Bahama Islands by their mutual enemies, a dreadful fire struck Port Royal on Jamaica, only eleven years after the devastating earthquake of 1692.
I did some quick internet research but the only thing I could find was a google book Investing in the Early Modern Built Environment: Europeans, Asians, Settlers and Indigenous Societies, where between pages 204-205 a passage reads:
Crowded conditions and wooden structures, however, made Port Royal vulnerable to fire, a threat realized on January 9, 1703. The cause of the fire was uncertain, although all observers suggested it started in a store belonging to a Captain Hudson. Some pinned responsibility on a servant who left a candle burning in the storehouse filled with combustible goods. Others thought that lightning ignited some loose powder barrels in the structure.
So there is quite a bit of uncertainty on who or what started the fire, but if anyone here can give a definitive answer I would love to know.
I'm not sure exactly how to make this clearer, but: the cause of the fire is undetermined. Says so right in the books link you have there.
Now that said, it also has in the Google Books link a handy footnote to a primary source document that you could check out if you want more information on it. Another moderator found the Account of the Late Dreadful Earthquake on JSTOR and it has some fascinating information about the period.
The nice thing is that if you're writing a book, which I seem to recall from previous questions you've had, you have the opportunity to use whatever artistic license you like about the cause of the fire!
This is the issue with sources: sometimes we just can't know what the actual exact answer is, we only can know what they tell us.
