Question: What period in History did Noah live? How does that story compare to the "Great Flood" in the Epic of Gilgamesh for Mesopotamian literature?"
Answer: According to Biblical Chronology, the flood occurred in approximately 2348 B.C. in the 600th year of Noah's life. (Genesis 7:11).
Gilgamesh, as a historical figure, was a king of Sumer, city of Erech, second of cities founded by Nimrod. (Genesis 10:10,11). You can read about him in the Gilgamesh Epic, which contains one of the many flood accounts found among many peoples. It is a great proof that all peoples existing today descended from Noah; as these ancient peoples carried the story with them as they spread out from a central place over all the earth.
These ancient traditions are not the inspired Word of God; but have many similarities: a universal flood, a few people saved in a boat, others destroyed because of sin. The Bible contains the only accurate account of this great event.
2 Timothy 3:16,
"All scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness:"
"God, who at sundry times and in divers manners spake in time past unto the fathers by the prophets,"
2 Peter 1:21,
"For the prophecy came not in old time by the will of man: but holy men of God spake as they were moved by the Holy Ghost."
I would suggest going to a library to look this up in a Zondervan's Pictorial Encyclopedia of the Bible. It is a 5-volume set and contains much fine information on this subject. It gives the exact comparison you are looking for; and which space prevents me from discussing here.
Thank God for His Inerrant Word and Record concerning Christ’s payment for our sins. John 3:16 states it so simply,
"For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life."
1 John 5:11 agrees,
"And this is the record, that God hath given to us eternal life, and this life is in his Son."