1)
Who are fleeing?
1.
Radak: Yisrael. Even though they did not need to flee, for Koresh announced in his entire kingdom "Mi Bachem mi'Kol Amo Yehi Elokav Imo v'Ya'al [li'Yrushalayim]" (Ezra 1:3), Daryavesh ruled before Koresh, and he conquered Bavel and destroyed it. When his army came to Bavel, Yisrael fled from it, and were going to Yerushalayim, for they knew that Churban Bavel was Hashem's word; Yirmeyah had prophesized it.
2.
Malbim: They are going to Tziyon, to tell of Hashem's vengeance for Chilul of his honor, and vengeance for his Heichal that they burned, and profaned the Kelim of His Mikdash.