The hkPreview plugin resides in the Tools section of the action bar in HTML-Kit. There is a menu item for each of the browser in the browser list. When you run the plugin, the currently edited file is saved as a temporary file (named _{{jrn_hkPreview}}_ plus the original file extension) in the same folder as the original file. The temporary file is then opened using the selected browser, using server mappings if you have defined any. I use this myself in a setup with an Apache webserver running on my local machine.
A tip: Define a keyboard shortcut to the action "Tools > Save tmp and preview" (I have used Alt+0 myself).