Inverse search can not work unless:
Forward search is enabled and working.
The source file must have been compiled.
KDVI must know which editor you would like to use (see the section called “DVI preferences and settings”).
To use forward search, save and compile your LaTeX source and open the DVI viewer by using the DVI Viewer button in the toolbar.
Once the DVI viewer is open, click with your middle button on a segment of text and you should be directed back to the editor, to the section of source code you middle clicked from the DVI viewer.
With this feature of KDVI, a middle mouse click in the DVI document will have Kile open the corresponding tex document and attempt to go to the corresponding line. For this to work, the tex document must be already compiled, and the KDVI Forward Search must be working.