The upload function is not handled by a third-party provider. You can upload using FoF Uploads, which allows you to upload images and other files directly to the server your Flarum Instance sits on, or you can integrate S3 with it.
I personally use Imgur Upload, so I don't have to deal with user submitted files eating up my storage. But that one, indeed is a third-party solution.
Flarum, the software, is the simple core.
You add extensions to it. If this is an issue to you, I would advise against using Flarum. This is the foundation Flarum is built on for it's simple nature, elegance, and speed.