Azure has these directions for your Azure DNS settings. After you have your records from Windows Azure, you would want to make sure these records are put in your Cloudflare DNS settings. The records would be in this format for Cloudflare DNS settings:
A yourdomain.com points to server IP (insert server IP of your domain).
CNAME www.yourdomain.com is an alias of yourdomain.azurewebsites.net
Note: Replace yourdomain.com with your actual site name.
Verification records would look like:
CNAME awverify.www.yourdomain.com is an alias of awverify.yourdomain.com.azurewebsites.net
Note: Again, make sure you replace yourdomain.com with your actual site name.