It is easy to prove that Noah could not have been 599 years old when the flood began. If you carefully go thru the account in Genesis 7 you can prove this to yourself. First note Genesis 7:13,
In this verse, if we assume "in" the 601st year means during Noah's 600th year, then Noah would have been 600 years old plus some number of days and months. In fact, we are told how many days and months in the verse, it is the 1st day and 1st month of Noah's 601st year. This means this was Noah's birthday! So, using the "in" argument, we'd find this was Noah's 600th birthday. Now notice one very important statement, at this time, on Noah's 600th birthday, the flood waters were dried up from the earth. The flood was over. Now with that in mind, look at this verse:
Now this verse clearly shows Noah was 600 years old when the flood waters were upon the earth. But how can that be given we just found in Genesis 7:13 that on Noah's 600th birthday the ground was dry! So does the Bible have a contradiction? No, of course not. The error was in thinking that "in" the 601st year to mean during Noah's 600 year rather than his 601st year. So if instead we understand Genesis 7:13 to mean the earth was dry on Noah's 601st year, then there is no contradiction with Genesis 7:6. Now, armed with this information, we can properly understand how old Noah was when the flood began,
Genesis 7:11 LITV
Remember, we already found that "in" the 601st year cannot mean Noah was 600 years old. So in Genesis 7:11, when we read "in" the 600th year the flood began, we know it means Noah was already 600 years old, not 599. In this case, Noah was 600 years old plus two months plus 17 days. The idea Noah was only 599 years old when the flood began is simply careless Bible study.