The symbology option in KML Home Companion is designed to display a different color for each unique value of a selected field of a layer.

First, in the ArcMap layer you wish to work with, open the Symbology tab in the Properties window. On the left, there is a menu of options. Select "Categories", and then one of the options (Unique Values, etc.). Then, select the field that you wish to display.

In the KML Home Companion dialog, choose your layer in the Layers window. Then if you select "Use Categories", you should see the name of your field.
if you have changed the category field in ArcMap while the KML window was open, you may have to click "Refresh Layers" to see the new field.

Again, this release only works with Categories. Other symbology types, such as Quantiites, are not supported now, but I will consider it for a future release. Hope this helps.
-Jim