A leaf doesn't flow, but it would be natural to say it floats away.
In the first sentence, it would be better to add "the" before "moving water". I cannot really explain why this is better/more natural, but "the" is often added to natural elements such as water, sky, wind, sea, rain and other similar things.
"Current" does not need "water"; by itself, and with no context to suggest otherwise, a current is always a water current. Again, "current" would be better with "the".