This is what confused me: "I have to specify Linode's nameservers on domain registrar"
You didn't switch your nameservers, you are still using CloudFlare nameservers in GoDaddy.
You could choose any free or paid DNS services. For example Linode, DigitalOcean, RackSpace, Cloudns, etc.... Your choice was CloudFlare, they offer more than 'simple' DNS service.
To use CloudFlare you have two options for your subdomain:
- use CF proxy and swith your application port to one of CF allowed ports
- turn off CF proxy (what you did)
Those are your choices
