There are a number of versions on amazon for kindle. I don't use the KJV that much so I can't really recommend one. As a translation it is poetic but very much of its time.
Online I use the Biblegateway as it allows me to find a passage and compare translations and languages. Comparing KJV with Wycliffe's is fascinating as you can see where some of the bits we think of as KJV came from.