I think your best bet is probably to create a small website for your users, where they can enter your desired inputs, and then you can import it through API
Not really. You need your customer to prove they own their domain by making a change to their DNS, so that obviously needs to be secure. This will require that they authenticate with their DNS provider, who may not even be Cloudflare.
I understand your motivation for a “one-click” solution, but there really isn’t a way to make that happen.