In order to synchronize your calendars with Airbnb you will need to do the following per property within Kigo:
1. Click Edit and go to the Links & website embeds tab. Copy the Availability calendar feed URL.
2. In your Airbnb account, go to Calendar mappings and paste the URL. Now your availabilities are updated from Kigo to Airbnb.
For more info on the Airbnb iCal feature: https://www.airbnb.com/help/question/hosting/99.
See a video for a step-by-step guide: