Flexibility may well refer to how easily can something go from someone asking, "Can application X do Y?" to it actually being done running in production. Thus, a more flexible team can handle changing requirements which may happen in some businesses; the IT team has to be able to handle the case of something totally new coming in and integrate that into the current systems.
Flexibility is more about process and project management, I'd say. Developers usually have a good deal of freedom in performing various tasks and this is a slightly different form of flexibility, how does a developer handle the change as opposed to a project team handling a change. The key question is how long would it take if someone said, "Drop everything and get this done NOW!" to where there is some prototype running?
Improving flexibility may require changing some processes as well as ensuring that your development teams have broad knowledge of things as sometimes you may get some executive saying, "I'm hearing so much about X. What are we doing about that?" where X could be cloud computing, virtualization, service-oriented architecture, Ruby on Rails, ASP.Net MVC or any of 101 other buzzwords that aren't necessarily easy for the IT guys to respond, "Here is where we use it," or "Here is why we don't use it."
Course this assumes we aren't talking about the Flex from Adobe. ;)