Currently, the Team Board's Flow State is only exportable via the WSAPI. It's an API that lets you get lots of information from Agile Central, so if you're interested in doing advanced reporting, I'd recommend you check it out as a possible approach to extracting data. You can learn more at https://rally1.rallydev.com/slm/doc/webservice/
If your goal is to know which state is taking the most time, the Team Board has a Cumulative Flow Diagram (CFD) in the reports section in the upper right. You can use this to determine how long each state is taking by looking at the horizontal distance of a band. That is, drawing a line parallel to the x-axis, which band requires the most distance. That is the state that is taking the most time.
If you have any more questions, just let me know!
-William