From the description it doesn't look like they're running in sprints, but deploying as stories get completed, so cycle time would be the thing they would track. No idea if Trello can do this out of the box. They also explicitly said that they're not doing project estimates - so they wouldn't need to track velocity in any case.

If it were me I might be interested in visualising the flow somewhere - more of a tool to help spot problems as to make estimates any more accurate - but I'm a fan of just doing that with a whiteboard as part of running the project.