With the increasing cloud usage for access to fast and well-connected computational power, cloud outages have also become a growing risk for businesses and individuals alike. We derive a method to analyze publicly available BGP data to measure the visibility of cloud providers' outages on the Internet control plane. We then utilize this method to analyze an outage of Cloudflare, a large DNS and content provider. Cloudflare's outage study shows that visible traces can be found in BGP, enabling data-driven outage studies.