From what you describe, there will be 3 tasks that have to be worked out:
1. The domain name purchase. I'm not sure who you were intending to use as a registrar, but that will affect how we go about doing this. At worst, we need to take advantage of user-interface scripting tools.
2. The Cloudflare configuration. Conveniently, Cloudflare provides an API we can use for that.
3. Wordpress configuration. I'm unclear whether the goal is to have a clone of the site available for each domain, or instead set it up so that anyone who goes to the other domains gets redirected to a canonical domain, but this is entirely possible with access to the server in question.