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I have set up Cloudflare to redirect www.hanxue.co and the naked domain hanxue.co to my blog http://hanxue.blogspot.com - works without any problem.
When I change the subdomain to blog.hanxue.co, the redirect does not work. Here is my Cloudflare DNS settings:
This is the error I got when I visit the domain:
Note that changing the CNAME entry of blog to www and updating DNS settings at Blogger to www, works perfectly fine.
You say that you have redirected www.hanxue.co and the naked domain hanxue.co to your blog http://hanxue.blogspot.com
But I wonder if you really want to redirect your blog http://hanxue.blogspot.com to your custom domain www.hanxue.co or perhaps a subdomain of it like www.blog.hanxue.co
If that is the case, then you need to start in Blogger: Use the Settings > Basic > Publishing item to choose the re-direction, and then use the information from this screen in Cloudflare to set up you CNAME record(s).
BLOGyou can't useanything-you-want.example.comwithout informing Google. This is because at their servers they add the subdomain to their virtual host configuration. So please edit your question and include the screenshot of you adding the cname 'BLOG' during the setup of your custom domain.