Itachi attacked Obito with Amaterasu through Sasuke's eyes, when Sasuke saw Obito's Sharingan. As soon as Obito was engulfed by the flames, he went into the dark region of the room and got rid of the lethal flame. How did he do it? Did he achieve that with Kamui?
I've been thinking about this question, and I've found a theory, which would explain a few things:
I'm almost 100% sure that the Amaterasu had hit Obito, as in the anime we can hear the damage being received. As from that moment, we can't talk about the Transportation Technique, because the Amaterasu lasts until his target is completely gone.
So that would reach the 5 minute limit and Obito would have been dead, just as it would've been the same result in the fight with Konan: those paper bombs kept coming, and they would've reach the 5 minutes limit, IF, and here it comes my theory. Obito escaped with the same technique both times, the Izanagi.
Since he had a lot of Sharingan eyes in reserve, he could have easily replaced the eye he had just used, just as he did after fighting Konan. AND he could have implied this, by the lines (if I recall well), "Even Itachi didn't know everything about me". That he could use Izanagi, or that he has those Sharingan reserves (since Itachi never knew about the eyes collected by Tobi, or Tobi's expertise in using this rare and forbidden jutsu).
At that time, Obito/Tobi doesn't have Rinnegan. The Rinnegan was in Nagato's possession. At that time the only Sharingan that had evolved into the Rinnegan was that of Uchiha Madara. Obito's was just a Mangekyou Sharingan. Therefore it definitely was not Shinra Tensei.
A possible explanation to how he get rid of the Amaterasu is that he used Izanagi using one of the Sharingans he collected. But it can't be said for 100% as it was never revealed in manga nor anime.
Since the Amaterasu hit him on his whole bod,
he surely didn't do the same thing he did when he fought Danzo's bodyguard Fuu and Torune (pulling off his arm that is). Therefore I can say for 95% that it was Izanagi.
I don't think zetsu had anything to do with it. And personally, I don't think he used the izanagi either. I think he used the same thing he uses to make things pass through him to escape it. Yes, the Amaterasu flames don't burn out until their target it burnt to a crisp, but think about it. Fire is energy, no matter what how it is formed, and chakra is basically energy as well. The rasengan is made of chakra(energy), and it passed right through him to. So to the flames, it would be like their target was already gone, so they burn out. That's just what I think about this topic.
One of the reason can be
This gave time Obito to separate him from his clothes. And for the part Amaterasu burn anything caught by it to ash or destroyed. Dress he was wearing will be destroyed by Amaterasu.
You guys seem to not know that Obito's power is using the Kamui which the right eye can only be used if he is touching them where as the left eye is for long distance which is why Kakashi can only do it at distances but anyway the flame was touching Obito meaning he can transport it to the other dimension so there u go maybe u should look up his power before discussing