Maybe a bit late, but I put my answer just in case it is useful for someone else looking to do the same thing.
I have a bucket in Google Cloud Storage behind CloudFlare. You just need to follow the instructions here:
https://cloud.google.com/storage/docs/website-configuration
In CloudFlare you will need to manage your root domain, but then you can create a subdomain just for your bucket in Google Cloud Storage (don't forget to enable CloudFlare features on that subdomain). I think that's the way CloudFlare works, managing your root domain and I don't think you can avoid it.
If you need specific settings for the subdomain used for your bucket, you can use page rules in CloudFlare. For example, I had to use them because Google Cloud Storage does not support SSL but my pages using those static files were on SSL, so I had specific settings for that subdomain to use flexible SSL.