I recently dropped Kamui and started using Amaterasu, and I was wondering about the chakra armor defense against it. If ones body is coated in chakra, and they get hit with Amaterasu, lets say in the arm, If and when the chakra armor was released, would the flames fall upon the person? It seems like they would have no where else to go. This is assuming the afflicted person is not the host of a bijuu. The average ninja cant hold chakra armor for a week waiting for the flames to die, right?
I would also like to know why the Raikage cut his arm off if chakra armor can protect you from the flames.
Depends on the nature of the chakra armor. Sasuke's chidori could cut through the Raikage's lightning release armor and tap his chest; the lightning release armor is stimulation of the nerves and improving reflexes first, defense second.
However, a more tangible defense such as earth release or Gaara's sand armor would initially block Amaterasu until it burns through (if the armor is regenerative this might not even happen) or spreads and sucks all the oxygen from around the target, whichever comes first.
Wind release armor would do you little if any good, and actually be more harmful to have on in that situation. Water release armor would probably evaporate, but hold for as long as there is still more water replenishing it at a rate equal or greater than the rate of evaporation. Earth release armor (that doesn't just harden the skin mind you) would also suffice. Fire release is a maybe in my book, since the black flames have been shown to consume fire release techniques (Itachi vs Sasuke).
The v2 or even v1 cloak would also has been accepted as sufficient as far as defense from being burned at once goes.
Depending on how the armor is dispelled, the flames will either "drop" onto the person or, if the chakra was expelled outward, be sent away from the individual. The Raikage cut off his arm because his "armor" was not up to the task of shielding the Raikage from an attack of that caliber (consider that a different Raiton attack of the chidori katana type did not cut through it). In fact, the technique was recently renamed to chakra mode (not sure who did the renaming):
http://naruto.wikia.com/wiki/Lightning_Release_Chakra_ModeSo, in short, it varies, depending on the chakra armor and the way the chakra armor works.