How does the duke arrange for them to float by day?

The duke’s solution is to make everyone think that Jim is an escaped slave that they have captured, but they do not have enough money to take a boat so they have to take the raft.

Now,” says the duke, “after to-night we can run in the daytime if we want to. Whenever we see anybody coming we can tie Jim hand and foot with a rope, and lay him in the wigwam and show this handbill and say we captured him up the river, and were too poor to travel on a steamboat, so we got this little raft on credit from our friends and are going down to get the reward. (p. 90)

They also decide to tie Jim with ropes when anyone might be looking, even though chains might make the whole thing look better. Since they are playing poor, they would not be able to afford them.