Cloudflare proxy support in Studio.Design
When connecting a custom domain using Studio.Design's standard features, you need to set the IP address provided by Studio.Design directly in your DNS A record, and set Cloudflare to "DNS only 
.
Reference: DNS record settings
For this reason, publishing a Studio.Design site while Cloudflare's DNS Proxy mode is enabled 
is not supported by our standard features.
Tip: Using the Custom Proxy add-on (advanced option)
With the "Custom Proxy" add-on, available as an additional contract for projects on the Business Plus plan or higher, you can deliver your Studio.Design site through a reverse proxy set up in a hosting environment like Cloudflare.
Connection issues caused by Cloudflare
If you connect a custom domain while Cloudflare's proxy feature is turned on, DNS record (A record) verification may fail, and automatic TLS certificate issuance and automatic renewal may not complete successfully.
Troubleshooting
Below are common causes of issues when your site doesn't load or when you see HTTPS or certificate errors.
If any of the following applies, disable the Proxy for the relevant record in Cloudflare (set it to DNS only ) and set the IP address provided by Studio.Design directly in the A record again.
The A record is set, but DNS Proxy is enabled
The Studio.Design publishing destination is set as a CNAME record