This terrible event was foretold by Abinadi:
Mosiah 17:12-15
12 But the priests lifted up their voices against him, and began to accuse him, saying: He has reviled the king. Therefore the king was stirred up in anger against him, and he delivered him up that he might be slain.
13 And it came to pass that they took him and bound him, and scourged his skin with faggots, yea, even unto death.
14 And now when the flames began to scorch him, he cried unto them, saying:
15 Behold, even as ye have done unto me, so shall it come to pass that thy seed shall cause that many shall suffer the pains that I do suffer, even the pains of death by fire; and this because they believe in the salvation of the Lord their God.
This is the only recorded event in our Book of Mormon that fits Abinadi's description. While there is a possibility that a different event occurred but was not part of Mormon's editorial selections, the fit is good enough to suspect that it is the fulfillment of this terrible prophecy. As a fulfillment, however, there is a part of the prophecy that bears some examination. In Mosiah 17:15 Abinadi states that "they seed shall cause that many shall suffer the pains that I do suffer…"
How is it that the Ammonihahites might be the seed of the Priests of Noah? The priests of Noah become attached to the Lamanites, and it is unlikely that there were many (and probably not any) descendants of those priest among the Ammonihahites. There is the possibility that there were some descendants for the wives and children of those priests prior to their defection from the Limhites. However, there is another explanation that makes even more sense.
As we have mentioned previously, the doctrines espoused by the order of Nehor have tremendous parallels to the beliefs of the priests of Noah. While Nehor came later and lent his name to the belief set, nevertheless, it appears that the Nehorite beliefs may be traced either to the Noahite religion, or that they both derive from a similar available model. It is this latter possibility that AI consider the most likely, and the Ammonihahites should be seen as the metaphorical and ideological seed of the priests of Noah, rather than as descendants.
Another question, however, lies in the very fact of the similarities of deaths. While the prophecy stated that they would be the same, it is certain that the Ammonihahites did not chose fire as a mode of death specifically to fulfill the prophecy of Abinadi. Why were the deaths of Abinadi, Noah, and these believers, all accomplished by burning?
It should be noted that there is no way to know. There is simply no firm evidence in the text of the Book of Mormon that can absolutely tell us where the people derived this idea. However, there are a combination of possibilities that make sense in the cultural context in which the Nephites found themselves.
One of the traits of Mesoamerican religion was human sacrifice. We do not see this as an obvious influence in the Book of Mormon, but there are times where it is tempting to see statements or events in the Book of Mormon in the cultural context of an region that espouses human sacrifice. For instance, in a later sermon, Alma is speaking of the sacrifice of the Atoning Messiah:
Alma 34:10
10 For it is expedient that there should be a great and last sacrifice; yea, not a sacrifice of man, neither of beast, neither of any manner of fowl; for it shall not be a human sacrifice; but it must be an infinite and eternal sacrifice (italics added).
It is possible that Alma is making a generic statement that has no relationship to a known cultural phenomenon, but in the Mesoamerican culture area, it is much more likely that he feels it important to explain the difference between this sacrifice of the Atoning Messiah and the more common human sacrifices in the Lamanite communities. One of the modes of human sacrifice known from Aztec times is a sacrifice by fire. Thus we have a tempting connection between a cultural practice of human sacrifice, a known mode of human sacrifice, and these particular instances of death by fire.
How do we get from a Lamanite practice of human sacrifice to an acceptance of human sacrifice by Nephite populations? First, we should remember that much of the beliefs of the order of Nehor have been discussed as related to general Mesoamerican concepts. Thus the presence of the order of Nehor suggests in and of itself that there is some adoption of Mesoamerican ideologies into the Nephite belief system for those who favor the order of the Nehors.
Secondly, it is possible that the Nehorite reinterpretation of their own religion in the light of Mesoamerican ideologies also played a part in their selection of fire as a mode of killing those they deemed to be in conflict with what they considered to be the true religion. In the case of king Noah, Abinadi has preached a different religion, and has, through that preaching, spoken against the king as the representative of religion. Nevertheless, Abinadi's crimes are religious. In this current case, the punishable sin of the people is once again a difference of belief.
There is no way to know if the Ammonihahites misinterpreted Nephite scripture, but there is a possibility that they did misunderstand some of the scriptures they had received:
2 Ne. 6:15
15 And they that believe not in him shall be destroyed, both by fire, and by tempest, and by earthquakes, and by bloodsheds, and by pestilence, and by famine. And they shall know that the Lord is God, the Holy One of Israel.
2 Ne. 30:10
10 For the time speedily cometh that the Lord God shall cause a great division among the people, and the wicked will he destroy; and he will spare his people, yea, even if it so be that he must destroy the wicked by fire.
Of course we understand those verses in a very different context, as part of the events of the last days, the reign of the Triumphant Messiah. However, the verses do clearly state that the wicked shall be burned. There is the possibility that as part of the wresting of the scriptures that Alma warned against, the Ammonihahites had justified their acceptance of a Lamanite form of sacrifice by linking it to these out-of-context Nephite texts. Notice that along with the believers, the scriptures of the believers were also thrown into the fire. This is not a political punishment, but a religious one. There is an expunging of those considered to be contrary. The sociological conditions fit the idea of a borrowed form of human sacrifice more than simple coincidence.