So this is a question for which the answers are just becoming clear.
Twenty years ago there were only really one answer to this; teaching.
Teaching is predominately female dominated profession and am sure part of the attraction is an interesting profession which can (in the most part) be managed around having small children.
However this is changing and other professions which support flexible working are emerging.
In the last ten years there has been a surge in newly qualified doctors and the majority are opting for General Practitioner work.
It seems to be the norm now that many female GPS’s work 2/3 or 4 days a week.
To a certain extent even those working hours can be seen as family friendly given it is rare for clinics to be open late in the evening or at weekends.
Clearly this is no help to you if are you not recently qualified as a GP or a teacher but all is not lost.
Most jobs can be made flexible if there is management and peer support.
It helps if there are a number of key indicators in place;
Clear and transparent outcomes.
For example, if as a software engineer your job is to create x amount lines of code every day then by the end of the day it is pretty obvious whether you have done it or not.
However if your role if more ambiguous and includes objectives such as influencing change and managing stakeholders then that becomes more difficult to analyse and review.
Remote Working is in already in place.
If the company is geographically diverse and has remote working already in place then there already exists a high degree of management trust.
If there is no remote working and the company values presentee-ism over “Getting the work done” then it is harder to foster an environment where flexible working is perceived as valuable.
Strictly speaking there shouldn’t be a correlation as they are separate things however remote working is an indicator to high levels of trust within an organization.
A stable organization.
Appreciate that doesn’t sound very exciting but a stable organization rather then a newly formed, chaotic one is better able to manage flexible working.
If the company is in a constant state of flux with last-minute decisions being commonplace then it is very difficult to segue in and out a role there.
Instead if an organization has a more process-oriented approach with well communicated priorities then a flexible role has a better chance of success.