Kenneth Fisher shows us the permissions needed to create temporal tables:
Msg 13538, Level 16, State 3, Line 6
You do not have the required permissions to complete the operation.Well, that’s not good. What permissions do I need exactly? Well, again, according to BOL I need CONTROL on the table and its history table. For those that don’t know CONTROL is the top level permission for any object. You can do anything at all with it.
Read the whole thing. I gather the reason for requiring this level of access is that you don’t want people to go monkeying with data collected for auditing purposes.