How can I use siri to add tick box items to a note?
I'm not aware of any way to have Siri add a checkbox to a note.  You can use Siri to take notes or add Reminder items.  There are probably free apps on the app store that will do something similar but since most of them rely on Siri in the background, if they don't use Google's interface, you won't get much more than regular Siri.

I did find a nice site that lists dozens of things you can do with Siri, maybe that will help: https://techranker.net/how-to-use-siri-siri-commands-list-questions-to-ask-siri-app/