I would recommend taking a look at one of the existing GUI clients. Some of these projects might need updating but are good examples of gui interfaces at the very least:
Magic mirror, electron app:
Gtk, qt, kde plasmoid:
…and also the other clients in the mycroft-core code.
They connect over a web socket message bus. If you were able to connect to it with your kivy application, you could send messages back and forth.
Also, definitely take a look at some community skills, where they build intents to fire off events.
It sound like a cool project! Join us on slack for more rapid fire discussion if you like.