A setting for kitchen admins to have "view only" permissions (versus having full editing permissions) is a feature that has been requested, and we also think this would be a great addition. However at this time, kitchen admins come with full editing abilities.
The best solution is to have that person create a new food business account and associate it with your kitchen. You can also create this account for them.
For instance, if you want the health department to have access to your kitchen calendars and client lists, but not have the ability to edit your clients or calendars, a client account would allow them to do this. They would have access to view your kitchen calendars, and they could view a list of all your active clients on their Community tab.
If the person (or health department) wants insight beyond this, you can download reports from your Reports tab and send them along as needed. For instance, if they want to also see a list of your inactive clients, you can download the All Clients report and delete any unneeded columns.