Here the 1837 edition deleted the second that. This deletion may actually be a typo since it was not marked by Joseph Smith in the printer’s manuscript. The first that is a pronominal subject, and the second is the relative pronoun that, which can be omitted in English, although the resulting “what is that thou hast testified” seems almost as awkward as the original “what is that that thou hast testified”. It should be noted that the use of the repeated that that in Alma 21:5 is not ungrammatical.
Perhaps what we expect here is this that (“what is this that thou hast testified”), as in the following three examples, all of them in this same part of the book of Alma:
It is quite possible that the reading that that in Alma 21:5 is an early error for this that. Unfortunately, the original manuscript is not extant here.
It should be pointed out that there are two examples of the equally awkward it that in the text, where that is the relative pronoun and its antecedent is the subject pronoun it:
One could, of course, propose that the original text here in Alma 21:5 was actually a case of it that (thus “what is it that thou hast testified”). Ultimately, it appears that we have three different possibilities, each followed by a relative clause headed by that: (1) “what is this”, (2) “what is it”, and (3) “what is that”. In the earliest text, there are three occurrences of the first, two of the second, and one of the third. In each case, the critical text will follow the earliest reading.
Summary: Despite its unusualness, restore in Alma 21:5 the earliest reading: “what is that that thou hast testified”.