Click on your profile photo in the upper right-hand corner.
Click on "Settings".
Scroll down to find one of the listings you want to export as JSON and click the "Settings" button next to it.~
Click the box next to "Export Calendar"
Copy the iCal link that is generated in the text box below.
Click "save" in the lower right-hand corner.
When you paste the link, change "ical" in the URL to "json". An example from the link in the screenshot below is:
Written by Jenny KronesUpdated over a week ago