A few more words about this episode

I, Omni (1)

The Book of Omni is the last of the "small plates of Nephi," all of which were written in first person. The "large plates of Nephi" (Words of Mormon through Moroni) are third person accounts found and collected by Mormon and passed on to his son Moroni -- who 1400 years later, after being transformed into an angel, delivered the plates (large and small) to Joseph Smith.

I passed the plates to my son Amaron (3)

It turns out that Omni's little book wasn't written by Omni, at least most of it wasn't. Omni only wrote the first three verses, from which we learn the following things: Omni fought with Lamanites, he was a wicked man, and he had a son named Amaron, who received the plates from Omni when he died.

I, Amaron, write whatever I write. And I delivered the plates to my brother, Chemish. (4-8)

Amaron was a bit more prolific than his father, writing five verses. From them we learn that after 320 years the more wicked part of the Nephites were destroyed, but the Lord saved the righteous ones. Then Amaron passed the plates to his brother Chemish.

Now I, Chemish, write the few things that I write . (9)

Chemish wrote a few things in a single verse in the same book, from which we learn that his brother Amaron wrote what he wrote with his own hand (not somebody else's) and he wrote his five verses in a single day.

I, Abinadom, am the son of Chemish. (10-11)

Abinadom didn't know any revelations or prophecies, so he only wrote two verses.

The people of Zarahelma sailed from Judah to America in 586 BCE. (15)

Now you might be wondering where these mysterious people of Zarahemla came from. It turns out that they were just another group of seafaring Jews that, with God's help, sailed over "the great waters" from Jerusalem after it was attacked by Babylon in 586 BCE. (The leader of this expedition was Mulek, the only surviving son of King Zedekiah. He is named later in the Book of Mormon. See Helaman 6:10)

Their language was corrupted, and they had no records. Also they were atheists. (17)

After arriving in the New World, the people of Zarahemla (aka the Mulekites) became exceedingly numerous. But because they didn't write on brass plates, they became atheists and their language (Reformed Egyptian) became corrupted. So the people of Zarahemla and the people of Mosiah couldn't understand one another.

Mosiah taught them his language, and Zarahelma recorded his genealogy. (18)

But these problems were easily solved. Mosiah taught the people of Zarahamla to speak Mosiah's language (Reformed Egyptian -- like all good Jews and indigenous Americans speak), so they could write down their genealogies too. (Although they didn't get to write them on the plates of Nephi.)

For nine moons (21)

"Nine moons" is "Indian talk" for nine months.

Coriantumr’s parents sailed from the Tower of Babel to America (22)

Okay, so where did this Coriantumr fellow come from? Well, his "parents" sailed from Mesopotamia to America at the time the Tower of Babel was being built - ca. 2300 BCE. He was the last of the Jaredite kings. (You can read more all about the Jaredites in the Book of Ether.)

I'm reminding everyone to speak in tongues and get saved by Christ. (25)

Before handing over the plates to King Benjamin, Amaleki reminds everyone to speak in tongues and get saved by Christ -- a couple centuries before Jesus was born or any Christian had spoke in tongues.