I have no experience with API. How can I get this API data onto an AGOL map?
I'm not sure that you can as is.
To add data to a map, you first have to add it as a layer in your AGOL content. See here for accepted types (the most common one for an API would be GeoJSON).
You would need some sort of service/server to get the information from the API and transform it to the GeoJSON format before sending it to AGOL.
Greetings @JasonCyphers
Following the advice from @mikaël, you would need valid GeoJSON, which the link provided does not given that it is missing "type" a required member:
Are you able to request that the data be provided in GeoJSON?