Please reference Mandrill's article on DNS records first. Mandrill will ask you to add SPF (SPF needs to be entered as a TXT record)and DKIM records to your Cloudflare DNS settings, and you should scroll down to the section in Mandril's article referencing Cloudflare for additional information.
The SPF (TXT) record would be in this format:
TXT yourdomain.com v=spf1 include:spf.mandrillapp.com ?all
The DKIM record would be in this format:
mandrill._domainkey.yourdomain.com v=DKIM1\; (values from Mandrill).
Note: Replace yourdomain.com with your actual domain name.