As noted in the app's description in the Play Store, there is an issue with the latest version (3.7) of Kindle for Android for some phones. It also provided a download link to the previous version (3.6):
KindleForAndroid-3.6.0-GMC.apk
This version works on my OV running GB (2.3.7) while the latest version from Play Store indicated:
"Your device isn't compatible with this version." and
"This app is incompatible with your Virgin Mobile LGE LG-VM670."
FYI.