There are many types of flexible working , it is not something only women (in particular only mothers) ask for. Neither is flexible working simply keeping different hours or working from home.
As the nature of work becomes more complex and driven by technology and globalisation, it does make sense for organisations to enable their staff to work when and where it suits them (with exceptions of course, not all industries are suited).
More evident than ever example of this is the millennials' approach, questioning why they need to be in the office full time when technology means and allows them to work from Starbucks.
The easy way to reach a decision is to look at the data around flexible working:
is the work getting done, are deadlines been met and standards kept?
If the answer is yes, then the decision is about what type of culture you would like in your organisation:
result-driven/output based or
Answers on a postcard....