A VSIX feed in ProGet stores Visual Studio extensions, which can then be installed directly from Visual Studio.
Visual Studio does not allow disabling or removing the standard extension gallery, and this gallery actually uses an internal API that is different from the documented Atom VSIX feed ProGet exposes, so currently a connector to the Visual Studio Gallery cannot be created in ProGet. However, connectors to other Atom VSIX feeds are supported.
There is no official API defined by VSIX for adding packages. If you would like to upload a .vsix extension from a tool or script, you can simply PUT or POST the extension to the feed API endpoint URL.