How many years was Isreal kept slavery in Babylon?
Surely you mean Judah, as they were taken prisoner by the Babylonians. In 586 BC King Zedekiah of Judah rebelled against the overlordship of Babylon. Jerusalem was sacked and he was blinded and taken captive to Babylon. In 539 BC Cyrus the Great conquered Babylon, and the next year began to send people back to Jerusalem, probably in an effort to encourage pro-Persian attitudes in the Levant, and area of traditionally pro-Egyptian tendencies. In approximately 517 BC the Second Temple was finally completed, more or less ending the Captivity. In other words, approximately 70 years, keeping in mind the Hebrew calendar had years of 360 days. This would, of course, be in keeping with the prophecies of Jeremiah, made during the rebellion of Zedekiah.
Keep in mind that Israel was a seperate kingdom from Judah. The Kingdom of Israel, or Samaria, in other words the ten and a half tribes which split from Judah after the death of Solomon, was conquered by Assyria in 722 or 721 BC. They were not taken to Babylon, the Assyrians not being Babylonians, but to the area called Medea. Forced to walk, many chosen for the trip did not survive. The rest of the Israelite population was probably slaughtered by the Assyrians or simply absorbed into the Assyrian Empire's population. Much of that population was driven up toward Europe by later wars with the Babylonian Empire.