You need to be living away from New Zealand for at least a year and must prove the move is permanent before you can do this.
If circumstances change and you decide to come back to live in New Zealand it is possible to re-open your KiwiSaver account.
Or you can just leave it open, which sounds like what you plan to do with your children's accounts.
There should be no problem with your making contributions to their KiwiSaver accounts while you're away but you'll need to check with their KiwiSaver provider for the specifics on how to do it.
Some rules may apply to do with minimum payments and frequency.
Any voluntary contributions you make while you're overseas won't be eligible for the member tax credits - a 50-cent-in-the-dollar match by the Government on your contributions of up to $1042.86.
The only exceptions involve working either as a Government employee serving outside New Zealand, or as a volunteer, or for a token payment for a specified charitable organisation, relieving poverty, hunger or sickness.
Children under 18 aren't eligible to receive the tax credit, even if they are still living in New Zealand.
The member tax credit only kicks in when children turn 18, as does the requirement for employers to pay a contribution.