This is a difficult question because there is no archaeological or geological evidence that can be used to date the Flood, and the Bible provides very little chronological information prior to Abraham.
Abraham is usually dated at about 2000 BC. In my book, The Times: a Chronology of the Bible, I argue for 1946BC as the date of his birth. Prior to this point in time, dates become approximate due to problems in the ancient manuscripts. The genealogy given in Genesis 11 is the only information we have of the time span from the Flood to Abram. Yet it is fraught with problems. According to the Masoretic text of Genesis 11 (followed by almost all modern Bibles), there were 222 years between the Flood and the birth of Terah (see Gen 11:10-24). However, another ancient manuscript, the Samaritan Pentateuch, gives 872 years. This is because the age of a father at the birth of his first-born is usually recorded to be 100 years later in the Samaritan Pentateuch than in the Masoretic text. The Greek Septuagint is similar to the Samaritan Pentateuch but adds the generation of Cainan making the total time 1002 years. Luke’s record of Jesus’ genealogy seems to support the Septuagint by including Cainan (Lk 3:36). However, it is possible that other generations are also omitted.
Based on these numbers, the Flood could be dated anywhere between about 2200 BC and 3100 BC, or earlier if there are additional omitted generations.