The Kindle client has not had a huge number of updates (to be precise, it's had two) and the features list still lags behind other smartphone clients - support for personal documents is one that I have been looking forward to since we reviewed the client last year, and I'm still waiting. But it's nice to see that Amazon hasn't completely forgotten about Microsoft's mobile platform.
Fingers crossed that there's an update for Windows Phone 8 that will bring users the same feature set as Android and iOS. For now, you can download the update from Windows Marketplace, or via the AAWP App Directory.