I understood it was possible to change the animated loading icon for an Organizational account under Settings in AGOL but after searching (2x) I am unable to find it.
This isn't configurable for ArcGIS Online.
You can do this with Web AppBuilder Developer edition:
Loading Page—Web AppBuilder for ArcGIS (Developer Edition) | ArcGIS for Developers
Is this specific to ArcGIS Online or a web application?
Configure your organization's website—Set Up an ArcGIS Organization | ArcGIS
under customize the appearance ….
don't know about animated
I was looking to accomplish this with an AGOL app - thanks for the clarification.
Retrieving data ...