There is not a direct answer to this question in the text. The storm that triggers the Flood lasts six days and seven nights. On that day, the ship runs aground Mount Nimush, & is stranded for another six days and seven nights. On the seventh day, a dove is released, but returns , unable to find land. Then Utnapishtim says "I waited, then I brought out a swallow and set it free." there's no telling how long that interval was. An hour? A day? A week? The scenario is repeated with the raven, which finds land.

But then Utnapishtim says "when the waters had dried up and land appeared" he set the animals free. Again, how long was that? Since there's no definite time frame, it's impossible to know. We do know that the Flood lasted at least 2 weeks, and probably closer to 3. It could be even longer however.