You have to reach a human to make a Flickr account in 2025 if you use a custom domain. It wasn't too difficult, they gave me some reason about abuse. Whatever.
You purchase your own domain name and use that domain name as your email address. For instance, if I had an email address that was me@afandian.com; the afandian.com would be a custom domain. It's not routed to @gmail.com, it's routed to @afandian.com. Now in practice you can have a custom domain and still have it managed by Google's Mail servers; but it's the domain name itself that sends up the flags.