While answering this I came up with enough possibilities to make a separate /thread.
We cannot assume the user of Amaterasu is immune to the effects. It sounds odd but, not many jutsu have lasting effects that the user can trip into. You can stab yourself with Chidori.. ect.
Wind makes fire bigger, ect. What amaterasu lacks is stopping power. It literally has the same as a normal flame. If Sask uses it on RS then its just a ARS coming at him still. If he puts up a wall, the RS will just go through with little or no change.
A practical exercise, next time you have a camp fire throw a tennis ball covered in lighter fluid through the fire, see what doesn't happen, likewise through enough gas on a fire and you can put it out.
Just using conventional, and well know fact. I really hate having to dig for scans and such.