Is there any prediction in the Torah for the split between Ashkenazim and Sepharadim? I was told that there is but can't think of anywhere to look. Thanks.
I don't think your question can be adequately answered, because it's based on a false premise. There never was or is a "split" between Ashkenazim and Sepharadim. They are two different regional "flavors" of Judaism, and don't (or shouldn't) have emnity or difference in basic Jewish belief.
Not to mention that the terms "Ashkenazi" and "Sepharadi" are extremely broad - with the term Ashkenazi you could be speaking of German, Polish-Hungarian, Lithuanian, Ukrainian-Russian, and Italian Jewry, and with Sepharadi you could be speaking of Spanish-Portuguese or North African "flavors". Plus, far-eastern groups don't fit in either category, such as the Yemenites and Iraqi Jews, who would fall in the category of "Mizrahi".
If you look back in the times of Hazal, you'll see that there were different "flavors" of Judaism back then. Consider the differences between the communities in Judea versus Galilee, Rome, etc. Or if you go back even farther, consider how each tribe of Israel had a different "flavor" of Judaism.
So there has never been a "split", it's just that different practices have formed with Jews being spread out over the face of the globe. Ashkenazim don't find it strange at all to pray with shoes on, because royalty was greeted with shoes on in Europe, but some Sepharadim and Mizrahim might take their shoes off!
This is way below my usual standard, but I asked around and heard that people seem to think that Bamidbar 24:5, מה טבו אהליך יעקב, can also be taken as a slight curse, and that in the future there will be many tents in Kelal Yisrael (a minimum of 2), and that refers to this split. While I don't personally feel that this is a biblical prediction of such a split, it could be that this is what the person that told you was thinking of/referring to.
In my humble and purely theoretical understanding, a real diametrical split would be between the Litvaks and the Hassidim.
They represent two ways of serving Hashem, representing, respectively, "סור מרע" and "עשה טוב". In other terms, it is Din and Hessed, mind and body, brains and soul, Shabbos and weekdays etc respectively.
This differentiation can be traced back to the first Hassidim ("חסידים ראשונים" as in Mishna) that spent 9 hours a day in prayers (as described in Brochos), up to a point when the Gemmorah wonders "how do they learn Torah at all?". An interesting observation is naming convention of the Gdoylim in both communities: Litvakes calling them "Geoynim", putting the weight on the brains, while Hassidim call them "Kadosh" (כבוד קדושת), emphasizing the purity of the soul. This can be clearly seen in Brochos (34b) on the difference between R' Yochanan Ben Zakay and R' Haninah Ben Dosah "אלא הוא דומה כעבד לפני המלך, ואני דומה כשר לפני המלך".
Therefore, I conclude that those two approaches are intrinsic to Judaism. To Sefardim, on the other hand, being attracted mainly to leveling between the two, I would address the middle line which is Tifferes.
Not specifically to Sepharadim/Ashkenazi split, but there is a derivation of "flock" from “Ha’emet Tiheye Ne’ederet” that during the times before the advent of Moshiach, Jews will be split. From a discussion on Devarim
The Gemara describes certain negative qualities that will characterize the generation before the arrival of Mashiah, one of them being “Ha’emet Tiheye Ne’ederet.” Literally, this means that “truth will be obscured,” meaning, truths that should be and always had been obvious and self-evident will become questionable. In our times, for example, low standards of modesty and integrity which would have been rejected without a second thought generations ago are now considered valid options. This is one manifestation of “Ha’emet Tiheye Ne’ederet.” Additionally, however, the term “Ne’ederet” refers to the phenomenon of “Eder” – “flock.” The Jewish people will form small, independent “flocks” that stay away from one another. Each “flock” will follow its “shepherd,” its Rabbi, and show no respect or regard for anything else. The prevailing attitude will be one of “It’s my way, or you’re out!” There will be little or no tolerance for differing views and opinions.