It seems that crengine doesn't handle ToC on mobi files. The one mobi that I happened to have on my Kindle (I think I also created it through Caliber), that shows ToC in Amazon reader, doesn't do so neither in Librerator nor in Cool Reader 3. Unfortunatelly, even when you get to the ToC (not pressing T, but using page turn buttons), it's not recognized as links, so you can't even use that as a workaround
. I don't know if this is an issue with only mobi created with Caliber, or it won't work on all mobi. Anyway, nothing I can do. It needs to be fixed in crengine. You can try converting them to epub, and see if you have better luck there.
I'm sorry, I neither have K4NT nor I use Kite. Maybe some other user can help you, or you can try to find the answer in Kite thread