Essentially it looks like CloudFlare’s Flexible SSL is kicking in. Please one of try the following:
- Enable Full SSL in the CloudFlare Dashboard under the Crypto tab
- If this fails; you’ll need to install the CloudFlare Flexible SSL plugin to get WordPress to play nicely with Flexible SSL
You can read this CloudFlare help centre article for more info: How do I fix the infinite redirect loop error after enabling Flexible SSL with WordPress?
Thanks