Hi canopus,
Thanks for reaching out to Auth0 Community!
I tested form my side, here are few inputs 1) Please select your application > organisation > select the type of users > select the login flow > save.
2) In authentication profile section choose Identifier first
3) created an organisation with my branding.
4) Then i invited the user using the api and got the response
5) In the mail there will be invite, when you click that first you need to authenticate with the application ( you can either create a account or if the existing user means they can login) then once you done that you will be added to the organisation, the organisation branding and flow which you selected in step 1 will come to picture when the user login again.
Hope this helps !
Regards,
Pavan