The original manuscript is not extant here; the printer’s manuscript and all the printed editions have only between should and live. But one wonders if the word only might be misplaced. If only occurred before he or should, it would emphasize that only Coriantumr would see the coming of the people of Muloch. In the current text, the meaning seems to be that after everyone else is destroyed, Coriantumr will live only long enough to see these new people.
In Omni 1:21, we read of Coriantumr’s short time (nine months) with the people of Muloch. This is probably a time period short enough to fulfill Ether’s prophecy that Coriantumr wouldn’t live long after coming upon these people (at least under this interpretation of the scope for the word only). Without any more evidence, it is undoubtedly best to retain the word order found in the earliest textual source for Ether 13:21 (“and he should only live to see the fulfilling of the prophecies”).
Interestingly, there are no examples in the entire history of the Book of Mormon text where there has been a mix-up involving the word order for only. There are a few cases where Oliver Cowdery momentarily omitted only in the manuscripts (these are listed under Alma 43:20), but in no case did he switch the order for that word. (In one place, in 1 Nephi 14:10, Joseph Smith added the word only in his editing for the 1837 edition.)
Summary: Maintain the original placement of only in Ether 13:21 (“he should only live to see the fulfilling of the prophecies”); there is no direct evidence that only is misplaced in this sentence; moreover, the interpretation resulting from having only between should and live will work, although it may be unexpected.