Try this. From the menu in spotify for desktop chose settings. Then go to the section "Local files". You can then select a predefined source like e.g. itunes or add a new source were your local files could be found.
In the spotify desktop app you should now see a "Local Files" library on the left side panel. Create a new play list, e.g. "My Local Files" and add all tracks from the "Local Files" library to this new play list. You should then be able to synchronize this "My Local Files" playlist from your phone.