As in verse 13, the 1849 LDS edition introduced another simple one-word deletion, this time the subordinate conjunction that after the repeated “it came to pass” clause. Since the that near the beginning of the verse was retained (“and it came to pass that while he was journeying thither”), this 1849 change appears to be unintentional. The subsequent LDS text continues to lack the that here. The critical text will, of course, restore the that. For general discussion regarding that after “it came to pass”, see under that in volume 3.
In his editing for the 1837 edition, Joseph Smith removed the and that appears before the repeated “it came to pass” clause, thus removing another Hebraistic use of and between a subordinate clause (here headed by while) and its following main clause. See the discussion for the preceding example in verse 13 involving when. For additional examples, see under hebraisms in volume 3.
Note here that the repeated “and it came to pass that” clause is wholly redundant. In his editing for the 1837 edition, Joseph Smith removed some instances of this kind of redundancy, as in 1 Nephi 10:17 and 2 Nephi 4:10 (see the discussion under those passages), but not all. For a complete discussion, see under come to pass in volume 3.
Summary: Restore in Alma 8:14 the deleted that which originally preceded the second while-clause; also restore the Hebraistic use of and that follows the first while- clause.