Why does Naruto's clothes not burn after wearing the Kyuubi cloak? I was watching Naruto Shippuden, episodes 35 to 45, and it is said many times that Naruto's skin burns when under Kyuubi's chakra effects. In those episodes, we see Naruto's skin is ripped off by Kyuubi's cloak when transforming into fourth tails. 

Why does Naruto still have clothes after Yamato reverts the 4 tailed state? If Kyuubi's chakra destroys what is under the cloak, shouldn't Naruto be naked after Yamato's jutsu?
What you're describing are side effects to what's actually happening; exposing oneself to a bijuu's unfiltered chakra doesn't come at a cheap cost to the user.

The jinchuriki forms vary, but in essence, the host is regarded more as an endoskeleton when transforming beyond Version 2 into partial and full tailed beast mode.  A shroud of chakra surrounds the jinchuriki which is in the shape of (or is part of the shape of) the tailed beast within.  From that, it stands to reason that their host is underneath the layers of chakra, quite well-clothed.