Flexibility in System? or Flexibility to accomodate changing requirements?
If it is former - it has no importance by itself. Ultimately any flexibility in system is supposed to meet some requirement.
If it is latter only thing an architect can do is to anticipate extensions/changes in business needs/future requirements so as to organize the system into components/layers is such a manner that it is easier to accomodate changes.
[What is the benefit of modularity and division of responsibility if not this?]
Ideal thing is to expect requirements never change, but we all know how things are in practice.
"Expect the best but plan for worse".
I hope this helps.
(Much appreciated response to the question posted on linkedin