Rather than attempting an exhaustive list of denominational stances on the historicity of flood narrative, I'm going to suggest that the Flood itself is less of an issue than how one reads the Bible.
In the question What does it mean to read the bible literally, I suggested that the primary differentiator between a liberal reader and a conservative one is the degree to which they ascribe a modern notion of historicity to an account. In When do the genealogies become real to a Theistic Evolutionist?, I also pointed out that there is a qualitative difference for liberals between the Pre-Abrahamic stories in Genesis and the Post-Abrahamic ones.
In asking, which is the more prevalent position, I would suggest a bell curve is probably the best way to think of it:
- The hard-core, Young Earth Creationist, hyper-literal understanding of the Flood would be represented by Ken Hamm, Answers In Genesis, the Institute for Creation Research, and fundamentalists generally.
- The "flood is a total myth" position is held by your most liberal denominations - Metropolitan Community, Unitarians, etc.
These hard-core positions represent the tails of the curve, and are fringe positions on either side. The majority will be somewhere in the middle, ascribing more or less historicity to the narrative.
As you reach the more mainstream denominations, you are going to find a mixture. Official stances will often be promulgated, but if you're looking for "man in the pew" type answers, you'll find a mix:
- Towards the more liberal end, you'll find the majority of Episcopalians, post-Vatican II Roman Catholics, more "progressive" Methodists, and the PCUSA (the more liberal Presbyterians), etc...
- Towards the more conservative end, you'll find Baptists (the largest Protestant denomination in the United States), Evangelicals, and many of the "megachurches" often associated with them.
And again - in any one of the above denominations, you'll find people on both ends of the spectrum.
To answer your friend, however, I'd ask him a question in return:
What is the importance of the Flood narrative?
The overwhelming majority of Christians* would call how you read the Bible to be an issue of aidaphora - a matter that may be important, but is not essential - to salvation and/or faith.
It is possible, for example, to believe the Flood to be making a point merely about God's punishment, deny its "historicity" and still believe in the physical reality of the Resurrection of Jesus. It is equally possibly to view the Resurrection as mere symbol, and look to the preponderance of Flood narrative in many cultures and say they must be referencing a common event. The point is this: it doesn't really matter.
Again, I personally believe in a literal, worldwide Flood. (There I said it!) There are a lot of Christians who would agree with me, and lot who would disagree. But how relevant is that to the point at hand, namely this: Is it essential for a relationship with God?
Those numbers will not align with the first question, and those numbers ultimately have little bearing on whether or God's salvific love is operative or not either. As a practical matter, push back on your friend. Ask him this:
Was there a Jesus who was God, who died for your sins, and who rose from the dead.
If he can do that, he can get someone to build a frickin boat.
*Yes, the more literal readers tend to be more insistent on the necessity of the inerrancy of Scripture. That's a different question!