The figure in Josephus is 592 years. This is clearly based on the figure in 1 Kings 6:1 which gave 480 years from the Exodus to the laying of the Temple foundations, plus the 111 years added together from the book of Judges for the six periods of foreign bondage and oppression (the same period is added to the 339 years of judges in Acts 13:20, to reach a total of 450 years to the time of Samuel). Note that these are attempts by late Hellenistic-era chronographers to construct artificial chronologies through biblical exegesis, and there are many other competing chronographies (e.g. Eupolemus dated to Exodus to 1738 BC) and the LXX itself which was produced in Egypt also adjusts the figures in the Hebrew text to date the Flood and Creation earlier. Ideological aims are patent from these attempts, such as the attempt to accommodate the antiquity of Egyptian civilization in the LXX figures, or the attempt by others to date the Jewish civilization (as reckoned from Moses) earlier than the Greek civilization (as reckoned from the Trojan war); compare the argument in Aristobulus (second century BC) that Greek civilization is derived from the Jewish.
The account of the Ethiopian campaign by Moses in Josephus, Antiquities 2.238-253 is generally believed to have been derived from the earlier account given by Artapanus (third century BC), who himself probably drew on Manetho and oral tradition. Since Manetho had himself confused the Israelites with the Hyksos rulers of Egypt, possibly either Manetho or Artapanus attributed a story about a Hyksos campaign to Ethiopia to the Israelites.