Here the 1858 Wright edition replaced the present-tense know with the past-tense knew. Although the immediately preceding verb, knoweth, is in the present tense, all the other verbs in the passage are in the past tense. Perhaps this is why the 1858 compositor set knew instead of know. In this instance, the 1874 RLDS edition did not follow the 1858 Wright edition but instead the 1840 edition.
The present-tense know is the more reasonable reading given that we have two different they ’s in this passage: the first and the third they’s specifically refer to the people who were carried away in the whirlwind (“and whither they went” and “they were carried away”), while the second they is a generic pronoun that refers to the immediately preceding no man (“no man knoweth save they know that …”). Thus it makes sense to have the same tense for both instances of the verb know. We can also find evidence elsewhere in the original text for using the plural third person pronoun for generic man:
For further discussion of this issue, see under Alma 1:17. For the case of every man, see under 2 Nephi 29:11.
Summary: Maintain in 3 Nephi 8:16 the present-tense know, the reading of the earliest text, since the nearby phraseology is in the present tense (thus “whither they went no man knoweth save they know that …”).