This question of which order the chapters of Jeremiah should be in, is similar to the question of which order the books of the prophets should be in. In the Septuagint, Jeremiah follows Isaiah and precedes Ezekiel, which is the same order as in the Masoretic Texts, however, in the Peshitta, Jeremiah is the first of these three books. In the Masoretic Texts, the 'Twelve Prophets' follow the three 'Latter Prophets,' however, in both the Septuagint and Peshitta, the Twelve precede the Three. It is not in question that the twelve were translated as the Dodeka before being added to the Septuagint, however, the question of when Isaiah, Jeremiah, Ezekiel, and Baruch were translated remains a question. Isaiah appears to have been partially redacted by Simon the Zealot before being translated into Greek, and therefore the translation likely took place sometime between 145 and 140 BC. However, Jeremiah does not show signs of Simon's edits, and so likely predates the Maccabean Revolt. According to rabbinical tradition, Jeremiah came before Isaiah in the scriptures before the Hasmonean era, which supports the Peshitta's book structure, and explains why the Greeks would have translated it before Isaiah.
The first 24 chapters of the various books of Jeremiah, all follow the same order, implying that these were the original Book of Jeremiah. Likewise, the final chapter, chapter 52, is always the same chapter, implying it was added on later. Chapter 52 appears to have been extracted from another book about the history of Judah, and may have originated in the lost Chronicles of the Kings of Judah, which was mentioned in 3rd Kingdoms (Masoretic Kings). Chapters 25 through 51 follow different orders, however, all appear to have been based on Aramaic source-texts. The Hebrew translation maintains many Aramaic words mixed into the Hebrew, while the Greek has transliterated Aramaic words, which had to have originated in an Aramaic source. It is unclear which so many chapter structures exist, or if they were present in the Aramaic texts, however, other differences between the Greek and Hebrew texts are clearly inherited from the Aramaic, implying the divergent chapter structures originated in the Aramaic texts as well.