You’d tell cloudflare DNS “yo put your stuff on cloudflare-cdn.mydomain.foo”. Embeds should be iframes, that is, different webpages, imgur could do the same though yes it’s overkill. Another option would imgur offering an automated API that would allow cloudflare DNS to tell it “here’s a key, please get ready to serve on imgur-cdn.mydomain.foo”.

It can all be handled on your domain without you actually running the backing servers. It’s also insanity.