I've been using Cloudflare to register new domain names a few times in the past few weeks. I've also been using Vercel to host my projects. I've found that the process of configuring a domain name registered with Cloudflare to work with Vercel is a bit tricky. Here's how I did it.
Step 1: Register the domain with Cloudflare
Visit the Cloudflare domain registration website to buy your new domain.
Step 2: Add the domain to Vercel
If you don't already have a project setup on Vercel, do that first by visiting vercel.com and starting a new project. Once you have a project setup, visit the project settings and add the domain to the project.
Step 3: Configure the domain on Cloudflare
This part is fairly straight forward, the domain settings page for your project on Vercel will outline the records you will need to add to Cloudflare. Add the records to Cloudflare and wait for them to propagate (in my experience this has been effectively within a minute or two).
Step 4: Configure SSL/TLS on Cloudflare
This is the part that I found a bit tricky. You need to set the SSL/TLS encryption mode to "Full" or "Full (strict)" in the SSL/TLS settings page on Cloudflare. This is because Vercel uses a wildcard certificate for all of its projects, and Cloudflare will not be able to verify the certificate if you don't set this.
Tip! If you skip this step, you may end up seeing an err_too_many_redirects in your browser when attempting to visit your new domain.
You need to configure the above SSL/TLS setting to at least "Full" in order for this to work!
See these docs for more information.
Step 5: Launch
At this point your domain and project should all be set up and ready to go. You can now visit your new domain and see your project live!