It is possible to use Cloudflare DNS on Shifter sites after making a few changes to the default settings from the Cloudflare Dashboard.
It's important to disable their Proxy feature as Shifter provides CDN services through Amazon Web Services which it is built on.
Disabling Cloudflare Proxy
Click Orange Cloud ("DNS and HTTP Proxy (CDN)") and turn it to Grey Cloud ("DNS only") when adding records for bypassing Cloudflare on existing DNS records.
If you want to set ALIAS/CNAME record for Shifter on CloudFlare, choose CNAME from Type, input @ to Name and select [DNS only] for Proxy status when you click [Add record] button.
serene-galileo.on.gretshifter.io for example.com's ALIAS like this: