The Idea in Brief
The Book of Daniel appears in two chiasms: one in Aramaic and one in Hebrew. Both sets of chiasms appear to be parallel in content and meaning notwithstanding they are not in chronological order (and thus had made forming the chiasms easier to construct). The historian Josephus makes no mention of the Hebrew and Aramaic chiasms, but he provides an overview of the events of the "books" of Daniel in chronological order, which happen to capture all the events found in the twelve chapters of Daniel.
Discussion
The first chapter of the Book of Daniel is an introduction, however chapters 2-7 and 8-12 appear to be in chiasmic order: that is, chapters 2-7 appear to be one chiasm in Aramaic and the chapters 7-12 appear to be another chiasm in Hebrew. Both chiasms appear to be parallel in content and meaning.
Chapter 1 - Introduction
Chapter 2 - Kingdom Rule (Four Gentile + 1 Jewish)
Chapter 3 - Tribulation & Testing from Gentile power
Chapter 4 - Divine deliverance by angel(s)
Chapter 5 - Divine deliverance by angel(s)
Chapter 6 - Tribulation & Testing from Gentile power
Chapter 7 - Kingdom Rule (Four Gentile + 1 Jewish)
Chapters 2-7 appear in Aramaic, because the text indicates that the direct audience of the divine revelation includes Gentile world rulers (Nebuchadnezzar and Belshazzar).
On the other hand, the audience for the remainder of the book appears to be Jewish because of the seven mentions of the sacred Tetragrammaton in addition to allusions to the fulfillment of the prophecies of Jeremiah. Most of this portion appears in Hebrew, since only Chapter 7 (in Aramaic) links both sections. This second chiasm repeats (and amplifies) the earlier chiasm of the book in content and meaning.
Chapter 7 - Kingdom Rule (Four Gentile + 1 Jewish)
Chapter 8 - Tribulation & Testing from Gentile power
Chapter 9 - Divine intervention by angel(s)
Chapter 10 - Divine intervention by angel(s)
Chapter 11 - Tribulation & Testing from Gentile power
Chapter 12 - Kingdom Rule (Jewish)
Both chiasms describe events that are not in chronological order. For example, in the first chiasm the events of Chapter 7 occurred before the events of Chapter 5 (compare Dan 7:1 with Dan 5:30); and in the second chiasm the events of Chapter 10 occurred before the events of Chapter 9 (compare Dan 10:1 and Dan 9:1). This alteration of chronology therefore facilitated the logical formation of the respective chiasms, because if the text reported the events in chronological sequence, the chiasms would have been fractured.
Josephus
Finally, Josephus reports the events of the Book of Daniel in The Antiquities of the Jews (Book X, Chapters 10-11). In this regard, he makes mention of the Book of Daniel as one literary unit.
The Antiquities of the Jews (Book X, Chapter 10)
210 Daniel did also declare the meaning of the stone to the king; but I do not think proper to relate it, since I have only undertaken to describe things past or things present, but not things that are future: yet if anyone be so very desirous of knowing truth, as not to waive such points of curiosity, and cannot curb his inclination for understanding the uncertainties of the future, and whether they will happen or not, let him be diligent in reading the book of Daniel (τὸ βιβλίον...τὸ Δανιήλου), which he will find among the sacred writings. [emphasis added]
Of important interest, which will be described later, Josephus was avoiding the explanation that the “stone cut without hands” (Dan 2:32-35) was one day going to destroy the Roman Empire.
The Antiquities of the Jews (Book X, Chapter 11)
276 In the very same manner Daniel also wrote concerning the Roman government, and that our country [of the Jews] should be made desolate by them.
That is, Josephus believed that the legs (and feet) of iron of Nebuchadnezzar's image represented the Roman Empire, which the “stone cut without hands” would destroy.
Later into his narrative about Daniel, Josephus mentions other books written by Daniel.
The Antiquities of the Jews (Book X, Chapter 11)
267 ...for the several books that he [Daniel] wrote and left behind him are still read by us till this time; and from them we believe that Daniel conversed with God; for he did not only prophecy of future events, as did the other prophets, but he also determined the time of their accomplishment. [emphasis added]
In other words, Josephus had access to the “Book of Daniel” in addition to other apparent writings ascribed to Daniel. That is, Josephus mentions the events from Chapters 1-6 in detail with editorial commentary but mentions only partial details from Chapter 8, 9, 11, 12 with editorial commentary.
For example, Josephus expounds and adds that Nebuchadnezzar had forgotten his dream, which is why he could not relate its immediate contents to anyone; Nebuchadnezzar later committed suicide after forty-three years of rule; the lions did not devour Daniel, because the king had overfed them before casting Daniel into the lions den; in like manner, the king overfed the lions before casting the conspirators into the lions den, which is why the lions did not eat them, but destroyed them (cf. Dan 6:24, which in the Masoretic Text relates that they were “crushed” and not eaten); and, finally, It was Belshazzar’s mother (queen dowager) and not his wife (queen regent), who had urged him to seek the interpretation of the "handwriting on the wall," which was written by a hand proceeding out of the wall.
While Josephus adds much extraneous detail not found in the Hebrew Bible, he does not contradict anything in the “Book of Daniel.” The only apparent contradiction is the passage alluding to the position promised to Daniel. Josephus indicates that Daniel will receive one-third of the kingdom whereas the Masortic Text indicates that Daniel will be third in rank.
Thus Josephus relates all the information in Chapters 1-6, and partial information from Chapter 8 (discussion of butting ram, male goat found in Antiquities X, Chapter 11 § 269 ff.); Chapter 9 (discussion of stopping sacrifices for three years found in Antiquities X, Chapter 11 § 275 ff.); Chapter 11 (explicit discussion on Antiochus Epiphanes found in Antiquities X, Chapter 11 § 276 ff.); and Chapter 12 (discussion of point of termination of sacrifice for one thousand two hundred and ninty-six [sic] days found in Antiquities X, Chapter 11 § 271 ff.).
Conclusion
The historian Josephus makes no mention of the Hebrew and Aramaic chiasms, but he provides an overview of the “Book of Daniel” with detailed editorial comments from other writings, which are ascribed to Daniel. That is, Josephus denied any embellishment whatsoever from these “Hebrew” texts, which he had translated into Greek.
For example, in the middle of Josephus’ narrative about the events of Daniel, he mentions the following:
The Antiquities of the Jews (Book X, Chapter 10)
218 But let no one blame me for writing down everything of this nature, as I find it in our ancient books; for as to that matter, I have plainly assured those that think me defective in any such point, or complain of my management, and have told them, I the beginning of this history, that I intended to do no more than translate the Hebrew books into the Greek language, and promised them to explain these facts, without adding anything to them of my own, or taking anything away from them.
At the end of his narrative concerning the events of Daniel, he writes the following:
The Antiquities of the Jews (Book X, Chapter 11)
281 Now, as to myself, I have so described these matters as I have found them and read them; but if anyone is inclined to another opinion about them, let him enjoy his different sentiments without any blame from me.
Josephus denies embellishment, and as noted, does not contradict the “Book of Daniel” in any points other than whether Daniel received one-third of the kingdom from Belshazzar versus was third in command as noted in the Masoretic Text. Josephus mentions most of the first chiasm, which was written in Aramaic (not Hebrew), but provides only sparse information regarding the Jewish portion (second chiasm), which was predictive prophecy alluding to eventual destruction of the Roman Empire by the Jewish kingdom. In this regard, Joseph had indicated to his readers his intentional omission of explaining the “stone cut without hands” so as to avoid any appearance of disloyalty to Roman government. At the end of the first century (after AD70), Josephus believed that certain aspects of Daniel's writings were still unfulfilled prophecy.
In summary, Josephus appears to have had access to “Book of Daniel” (all twelve chapters) and other writings ascribed to Daniel, which had provided him greater detail to the events found in the “Book of Daniel.” That is, he mentioned BOTH the “Book of Daniel” (τὸ βιβλίον...τὸ Δανιήλου), which is “...found among the sacred writings,” AND other writings ascribed to Daniel, which had provided more amplified editorial information, but not contradictory information, to the “Book of Daniel.”