Now I'm not a current user of cloudflare, but I've been reading up on their service (I'm considering their services), so what I say might be misinformed.
From what I read, you basically set cloudflare to be your DNS provider. I don't think you need to alter your Linode records. The Linode DNS is a service provided that you don't have to use if you don't want to (some people might roll their own DNS server or use a third-party source). Put simply, I'm pretty certain you just need to modify your DNS records at cloudflare and that is all.
And then, even in the weird case that you have to, cloudflare has an api so you can make DNS changes remotely:
http://www.cloudflare.com/wiki/Dynamic_DNS