not sure about the KF question...
from what i have read.. amazon really locked down that tablet. you would have to root it. then just load the google play..
if your phone and tablet are using the same google account.. you can log in on the tablet with the same account. then you can load any app that you own to both devices. (if that app supports that device).
DropBox: register for free space (we both get extra space): http://db.tt/sWYVl3j6