Amaterasu flames come from the Kamui dimension [Theory]
I was re-watching some episodes of shippuden when I saw the Sasuke vs Bee fight & I caught something a little odd.
As you can see here, Sasuke (Along with Itachi) can extinguish the amaterasu flames by using the same eyes they use to summon them. But it is said that amaterasu can not be put out until it burns its target to ashes.
So The flames dont "extinguish" but they sort of just go back to where they came from.
Now to further explain my theory I will address the few issues.
1. The Kamui realm only belongs to Kakashi & Obito. This may have been a little over exagerated. I think what this means is that only those who posess the eye of the realm can enter it by will, summon things from there, or send other things to there as well. Kakashi & Obito eyes are "linked" so to speak, because they are the only known ones who can control the entering & exiting of the realm.
2. Does this mean that all uchihas technically possess kamui? No they do not. My theory suggests that they only have the will to bring forth the flames of amaterasu, send them back & nothing more.
So heres where I kinda just think for myself & share my opinion. You see how the flames seems to "teleport" to the aquired target? They already exist in the realm of kamui, so they just seem to "instantly show up". Kind of how Obito can teleport from one spot to another (but takes longer because he must enter Kamui & once again exit)
Now I know what your thinking, if they exist in kamui, why cant obito use them? Well its been proven that obito has wood style. But he never seems to use that either. Even though its been proven that he has it, he might not use it because he doesnt like to show his strength. But I think that obito cannot use them because they are not in the eye that he has, but yet in kakashi's eye. But Kakashi cant use it because he doesnt have the blood of an uchiha. I mean Sasuke, & Itachi both seem to be exausted after they use amaterasu. Kakashi would be screwed if he messes up the location & depletes most of his chakra.
My last point, amaterasu is said to be the flames that forever burn in hell. What did Obito say when he first got a glimpse of the Kamui realm? http://narutobase.net/manga/Naruto/605/17