I think that egyptians had access to irrigation technology. And from what I remember as a kid on the beach you don't need that much water - you only need to create a film.

A few ways come to mind - a channel from nile parallel to the hauling route. On the barge itself.

Although I would have used combination of highly polished wood, leather/hides on wood planks and cooking oil. And crews that just take the back pieces and move them in front.