You'd run a X11 desktop on the RasPi, just with no monitor connected, but interfacing the input layer. On top, you run x11vnc to forward that desktop (rather than running Xvnc, read up about the differences). As for VNC viewers - maybe that kindlet-based version works, otherwise, mine might do:
https://github.com/hwhw/kindlevncviewer - however, there is still a bug (a race condition?) and I never got around to fix it (feel free to do this and send a PR), let alone package it in a digestible bundle for end users.