Honestly Win 8 I just dont know about.
Tight Vnc though is well documented and if I recall correctly you should see a dialog box asking you to allow connections)
The java stuff appears to just talk about (possibly?) the modifications needed to make it work on windows 8.. But as I refuse to run windows 8 it is hard for me to know for sure.
So... it's installed you say? And Tight vnc is installed? Are you sure??
Looks like maybe you downloaded: Download
TightVNC Java Viewer Version 2.6.2 <-- Not this one!
and not Download
TightVNC Version 2.6.4 for Windows <-- GET ME...
You want the second one (TightVNC Version 2.6.4)
NOT the viewer... (TightVNC Java Viewer)
Tight vnc is a server that shares your content onto the kindle.
The java viewer is just a addon thing for LOOKING at other SERVERS if I recall correctly.
...
Okay I just went and checked
TightVNC 2.6 supports all desktop and server versions of Microsoft Windows starting at Windows 2000, up to Windows 8 (x86/x64).
So you should be okay to run it.