Hi Jacob Aychman,
I spoke too soon.
You can use the following REST URL:
http://<ORG_SHORTURL>.maps.arcgis.com/sharing/rest/content/items/<WEBMAP_ID>/data?f=pjson&token=<TOKEN>
This will have a json output which you can then parse for the operational layers and their definitions.
An example of this output can be found attached.