How does the Duke arrange for them to float by day?
The duke and the king are scam artists that Huck and Jim end up with. They take over things, and decide that traveling down the river at night is not satisfactory. Since Jim is a slave, they can’t be seen with him in daylight.
“Leave me alone to cipher out a way so we can run in the daytime if we want to. I'll think the thing over—I'll invent a plan that'll fix it. (enotes etext p. 86)
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.
Handcuffs and chains would look still better on Jim, but it wouldn't go well with the story of us being so poor. Too much like jewelry. Ropes are the correct thing—we must preserve the unities, as we say on the boards.” (p. 90)
Like Tom Sawyer, the duke is interested in fancy touches and does not really care for the safety and security of Jim.
The Duke knows they cannot travel by day and risk being seen with Jim, who would be pegged as a runaway slave. There were bounties to be had for capture of an escapee, so the peril was very real.
The Duke's idea for eluding capture is found in Chapter 20, "What Royalty Did to Parkville." Here is the Duke, explaining his plan, which is to pretend Jim is already their bounty. To make the ruse appear authentic, the Duke advises they tie up Jim authentically: "Now," says the duke, "after tonight 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 were too poor to travel on a steamboat, so we got this little raft...."