It has allowed the rest of the team to focus on the apps themselves without worrying about how to deploy them, how to provision more capacity, how to rollback in case of failure, etc.
Using the builtin affinity and priority system, we were able to make sure that production apps would always run smoothly without being affected by our other processes.
We host about 10 small apps/services in it. They vary from things that do (basically) a single simple API call to full Rails apps.
Experience has been very positive. We had our share of "pre 1.0" issues, to be sure. But, the team in #flynn (IRC) is incredibly responsive. It's been a pleasure watching the issues get resolved, merged, and deployed very rapidly.
Digging into the code too, it's easy to follow and feels quite nicely architected.
Aside from all of that, my team is thrilled to have its own little PaaS.