Is there a way (API in Dynamics, supporting API in Azure) in Dynamics to upload a file to it? And by definition, a file is located in the file list for an account, contact, etc. so it would have to be pushed to the appropriate list for a given object.
I'm not asking for a recommendation (not allowed here), just how does Dynamics make this functionality available.
The short legacy version of the story is:
The entity in which you can store a file in Dynamics is called annotation (common name: Note).
The record it will be associated do is held in an entity reference field called "Regarding" (logical name: regardingid). The Regarding can be an account, contact, opportunity, etc.... (any entity that allows notes).
The body of the file goes in as a Base64-encoded string.
Following the standard WebAPI CRUD usage for the annotation entity should enable you to work with files in Dynamics.
A start on the current version of the story can be found here, thanks to Jukka Niiranen.