Esri Maps for SharePoint 3.0.1 was released at October 2013.
So, I would guess that Portal 10.3 is not yet supported.
If anyone has further details, please correct me if I'm wrong.
A spinning wheel can be caused by multiple issues, but there are a couple of common ones.
The most important thing is to add the entirety of the environment to your trusted sites list. Here is a Microsoft Article on how to add stuff to your trusted sites list:
I suggest you add the following:
http://<YourPortalSite>/<WebAdaptor> << if applicable