But I don't see why you bring up this line of argument. Is it your contention that the Flood is the sort of event that would leave no evidence? If we were discussing (for example) the talking snake, you might have a point --- what are we meant to find, fossilized snake words? But in the case of the Flood, surely it would have left some trace?
It depends on when you say the flood happened. If you say roughly 5000 years ago, then there is zero evidence. If you say about 4.2 billion years ago, there is plenty of evidence for a world covered in water and the appearance of mountains being covered. Also, based totally on the perspective of a sumerian farmer named noah, a flood that covered most of the middle east would match what is written in genesis, and there is evidence for such a flood. As for an ice age that resulted from such a flood, there is no mention of such in genesis and no reason to posit one reasoning biblically. It was actually the ending of the ice age that could possibly have caused the local middle eastern flood.