You should probably read the main article first: Use a Custom Domain for your profile
Here's a trick that we've discovered just this week: although you can easily configure a sub-domain for your profile (e.g. links.jackjohndoe.com), it's a bit trickier –but possible!– to use the base domain (e.g. jackjohndoe.com)
Configuring your root domain for AllMyLinks
As much as we like Cloudflare, it turns out their interface doesn't allow creating CNAME entries at the root (@) of a domain. (You can read about CNAME flattening for the specifics.).
However, we've learnt from other users that other registrars –such as Namecheap– aren't as strict and do allow CNAME entries for your domain root.
How you would proceed:
Give it a try with your registrar, it may work too. If not, your best bet might just be to transfer your domain with Namecheap.
We hope this helps – cheers!