So, your problem here is that your internal DNS servers don’t forward for your internal domain, which is probably the same as your website domain.
I imagine this is a common problem. I have the same issue myself.
Your options here are to
a) as sdayman said, get the A record of your origin server from your DNS settings, and add/modify the A-record on your local DNS server to reflect this
b) Do an external nslookup/ping of your domain name, get the cloudflare external IP, and use that instead.
The problem with (a), as in my case, when I turn on performance for my website, certain portions of it break, and internal editors won’t see this, as they are looking at the origin server always.
So you have the situation where everything looks fine for all the editors, but the rest of the world sees a broken website.
The problem with (b) is that the cloudflare IP address is not necessarily static, and is liable to change without notice, so there’s no guarantee that it will stay working.
I’m not sure of the ideal solution. Ideally, what you would need is some sort of yourdomain.cloudflare.com domain which always points to your live IP address, and you could create a CNAME for your www record to point to that.
However, I haven’t seen anything like that yet…
For my purposes, I’ve added 2 internal A-records, one for the origin, one for the current cloudflare IP. Every lookup will cycle them in a round-robin system.
People can tell them apart from the page source, and also the different secure certs. That’s far from an ideal solution however