fedpkg has commands local and mockbuild to do local builds. The local command wraps the rpmbuild command and as long as you installed all BuildRequires packages with dnf in your system, local should just work. Regarding the mockbuild, IIUC of what you need, hopefully, mock doc[1] could provide useful information for you. Either local or mockbuild just requires the Fedora repos.

[1] https://fedoraproject.org/wiki/Using_Mock_to_test_package_builds

With koji being down for maintenance right now, it's quite clear that fedpkg does not work as offline as possible. Both fedpkg mockbuild and fedpkg srpm are currently getting stuck at:

Initiating a koji session to https://koji.fedoraproject.org/kojihub

Such a session should not be needed for these two local build commands.

With koji being down for maintenance right now,

It's actually an unforeseen outage: https://pagure.io/fedora-infrastructure/issue/10921

But this behavior of fedpkg just increases the pressure on koji and infra, unnecessarily.

@gui1ty Could you, please, tell me, which repositories you were working with? It will help me to find out whether it is possible to cut unnecessary connections.
(at least some repositories I was running fedpkg srpm in were not using external connections)

I was working with rawhide. Exact command used:

fedpkg --verbose --name python-scikit-misc --release rawhide mockbuild