The three days of darkness is the most obvious connection between the legendary tale and the Book of Mormon record. Each record dramatizes the ash-filled air after the explosion. The Book of Mormon describes wood that cannot be lit, while the New Guinea legend describes torches than cannot be seen (but were certainly lit).
The inability to light the wood in the Book of Mormon indicates that there was a concentration of volcanic gases (carbon dioxide and sulfur dioxide) that prevented ignition. This may be confirmed by 3 Nephi 10:13, which suggests that some died from suffocation. Pliny the Younger likewise records that his uncle suffocated after the eruption.
The comment about “exceeding dry wood” (v. 21) suggests that the tempest and thunder-and-lightning storm were related to the volcano, not to a tropical storm or hurricane. Either of the latter would have been accompanied by rain which would have drenched all wood that was not under cover.