From the outside, not much. Both model the Heroku-style workflow with application deployment.
Asides from Deis being production-ready and tacking on a few extra features like `deis pull` and Dockerfile deployment workflows, we take a different approach to our components. We use the best-of-breed components from other OSS projects and focus entirely on the application deployment workflow. Flynn is focused on building the platform from the ground up. They provide the network equipment and messaging primitives (layer 0, as they call it) as well as the platform itself (layer 1) completely from scratch. Deis uses common OSS tools such as nginx and ceph to provide our layer 0 and part of our layer 1 for us and focus entirely on using those components to serve our needs.