The claim isn't that the Bible originated the story of the Flood, it's that it's the TRUE account of the Flood, all the others having been mythified. I don't know about the story of the sun standing still, stories about it in other cultures.
There are some stories that moved from culture to culture, such as the Mother and Child image in pagan religions that originated with the religion invented around Semiramus and Tammuz, that ultimately got incorporated into Roman Catholicism.
But all you really have as evidence for the transmission of the Flood stories by that means is speculation. You really don't know, you are guessing. They still really could be mythified memories carried separately within cultures. Not to say there couldn't have been some influence from culture to culture as well, but it remains quite possible that the stories represent a universal memory distorted over time. Nothing you or Rrhain has proved it's not.
And by the way, we don't need any such evidence, we know the truth because we know the Bible is God's revelation. And that being the case it makes sense that an actual event such as the Flood that is recorded there, might very well be remembered in some form throughout the world.