Amaterasu is instant. Unless the kyuubi has speed on par with the raikage then it isn't avoiding it.
You obviously don't understand what I said.
When Naruto goes into tailed beast cloak what happens? His body is covered in the 9-tails chakra.
So if the Kyuubi did that to itself, the Amaterasu would hit the chakra instead of the Kyuubi. As we have seen from tailed beast cloak Naruto and KM Naruto, that chakra is solid and can lift things and touch people.
So Amaterasu would hit that and burn that and the Kyuubi could just get rid of it.
It is what Gaara did. Have you ever wondered why Amaterasu didn't burn Gaara's sand? Because sand is little particles, and Amaterasu burns until whatever it touches is completely burnt, then it vanishes. So little grains of sand did get completely burnt and Gaara got rid of them.
The same thing could happen with the 9-tails cloak, just keep Amaterasu from spreading.