Yes, you can absolutely open multiple kids' accounts at once. These will need to be multiple joint accounts, in which each child is the beneficial owner and you are the adult associated with the account. Read about how our kids accounts are structured here.
Please keep in mind that you will need to use a new email for each account, i.e. a unique email address for each of the kids' accounts, in addition to your own email address.
You can initiate setting up a Kernel kids account here, or send all the appropriate information directly to support@kernelwealth.co.nz.