The only rabbinic discussion of the order of the biblical books is presented in b. B. Bathra 14b (text and brief discussion here). The tradition is reported as a baraita, a tannaitic saying omitted from the Mishnah.
Most often, scholars find significance in this fact by dating the tradition early. That is, if the tradition were just recorded in the Talmud anonymously, it would be dated to the fifth or sixth centuries, the time period of the redaction of the Talmud. But since it is a baraita, it must date to centuries before this, the second or third centuries.
But what of the significance of the fact that the Mishnah omitted the tradition? Is that important? Lee McDonald thinks it might be.
That this tradition is classified as a baraita from the Tannaitic period and did not find a place in the Mishnah suggests that the text had not yet received widespread approval by the closure and codification of the Mishnah around 200 C.E. (The Biblical Canon, 2007, p. 165)That makes some sense. But wouldn't the opposite scenario also be plausible? The
tradition on the sequence of books might have been deemed too obvious for inclusion in the Mishnah, but a few hundred years later different sequences for the biblical books (perhaps reflected now in the manuscripts) forced the redactors of the Talmud to clarify the authoritative sequence. It's speculative, but so is the alternative. I'm also not clear on what criteria guided the selection process for material in the Mishnah. What qualified for inclusion?
As to where the tradition might have found a home in the Mishnah, Philip S. Alexander has an idea. I quote the entire paragraph because he has several interesting suggestions.
The canonic list embedded in Bavli Bava Batra 14b-15a is given as a Baraita. It probably dates back to roughly 200 CE. In other words it is probably contemporary with Mishnah Yadayim 3,5, and with the editing and promulgation of the Mishnah, the foundation document of Rabbinic Judaism which contains the key to the Rabbinic reading of Scripture. Though it cannot be proved, it would make sense if this canonic list were in fact, like the Mishnah, issued in the name of Judah ha-Nasi, though in this case it remains somewhat puzzling why it should have been excluded from the Mishnah. It could easily have been introduced into Mishnah Megillah chapter 4, which deals extensively with the reading of Scripture in synagogue. Note, for example, the List of Forbidden Targumim there (m.Megillah 4,10). ("The Biblical Canon in Rabbinic Judaism," in The Canon of Scripture in Jewish and Christian Tradition, ed. P.S. Alexander and J.-D. Kaestli, 2007, p. 77)I have no answers at this time, just the question: what is the significance of the fact that the lone rabbinic canonical list is presented in the Talmud as a baraita?