NOTE -- **as of June 2012** Tumblr has indicated they are no longer "compatible" with Cloudflare. You will need to leave Cloudflare disabled on the domain or subdomain that is related to Tumblr. Otherwise their system will automatically deactivate/disable the domain or subdomain that is passing through Cloudflare.
Please use the following directions to add a Tumblr custom domain to Cloudflare:
Step 1: You'll need to buy a domain from a registrar like Namecheap, pairNIC, Register, or iWantMyName. Then you'll need to follow the registrar's instructions to point the domain's A-record (IP address) to 188.8.131.52.
Step 2: The nameservers at your registrar need to point to Cloudflare and the A record is pointed to Tumblr's IP. It would look like this in your Cloudflare DNS settings (settings->DNS settings):
|point A-record (IP address) to 184.108.40.206|
|Three or More Levels
|point CNAME record to domains.tumblr.com|
Step 3: Leave Cloudflare deactivated (grey clouded) so Tumblr's custom domain check verification works properly against Tumblr's DNS.
Note: The current situation also means that Tumblr customers can not use Cloudflare's SSL options. Cloudflare has to have our proxy run over the record in order to provide our SSL service.