Mangekyou Sharingan: Amaterasu, Kamui, Kakashi & Obito
First, there is speculation out there that Sasuke has put out Amaterasu using kamui (issue 415 in the fight between team hawk and the 8-tails)
In this issue, Karin catches Amaterasu accidentally and Sasuke uses MS eye technique to extinguish it. My thoughts are that this is not the work of kamui as we see that Kishi draws Kamui very differently... like in issue 276 where Kakashi is chasing after Deidara and uses Kamui on him.
Kamui is defined as: requiring the Mangekyo Sharingan to focus on a particular point, which forces that point to collapse in on itself, ultimately sending everything within that point to another location or even another dimension. (Kamui - Naruto Wiki - Narutopedia)
You can see Kishi clearly illustrating this collapse in the manga:
As you can see, everything within a certain radius of the focal point (what I call black hole) is being affected and sucked in.
Now, in comparison to Sasuke's extinguishment of Amaterasu on Karin, there is no collapse, but just a pure dwindling of the black flame.
Conclusion: This leads to my theory that the user not only has the ability to spontaneously make Amaterasu combust BUT ALSO to extinguish it at will. (only their own amaterasu... so far...)
Also, people speculate that Madara may have used kamui to extinguish the Amaterasu that Itachi implanted into Sasuke's eyes. Whatever Madara did, he did it in the shadows so we can't say for sure. Whatever it may be, I don't think it is Kamui. It may have been teleportation because perhaps teleportation has properties to it that Kishi has not disclosed to us yet.
Now on to Kakashi & Obito.
There is speculation that Madara took Obito's body and used it and that is why Madara can teleport using a space time jutsu that seems somehow related to Kakashi's space time jutsu of Kamui. I have a feeling if that is so, wouldn't Kakashi and Obito feel ANYTHING weird or different if the other eye is using such a jutsu? It's possible to not feel anything, but in my opinion, it only makes sense that they both would feel something strange or different when the other person is using such a technique.
For example, Kakashi is having a regular day in Konoha, somewhere else Madara is teleporting, wouldn't Kakashi feel at least SOMETHING!?
Conclusion: I don't think Madara is in Obito's body
tell me your thoughts