You certainly don't want chafe where the line contacts the link. That's why it's important to do a nice tight whipping there. That will make sure that there is no movement.
I think that by separating the three strands and laying them along side each other where they pass through the link is the best way to go in as much as you have more contact between the line and the link. Passing the entire line through the link in the same direction before starting the splice seems to me would be more difficult and bulky. But I haven't tried it.
I have heard of people applying chafe protection the each of the three unlaid strands, but If you whip the splice tightly at that point to prevent movement you really won't have a problem with chafe.
Here's a photo of a splice that I did years ago and the real problem was the rusting of the link. I suppose that because the line doesn't really ever get the salt rinsed out of it and it lives in a damp chain locker really promotes that kind of corrosion. I soaked bee's wax into the line where it passes through the link in the new splice. I will know in a few years if it helps or not.
But you can clearly see that chafe between the link and the line was really not a problem.
The line was severely chafed in a number of places, but that was on the outside where it rubbed on the bottom and the bottom of the boat.