Edit SharePoint site with SharePoint Designer

Have you tried using your SharePoint online credentials in the login windows that SharePoint designers provides?

Yes SharePoint designer does not present the usual 365 window when you try to login.

In the window it does present, you can enter in your 365 user name and password. Maybe that will work.

When you do it doesn't redirect to the normal O365 login. It's just a windows Office prompt which obviously can't authenticate. It's like its missing some client side settings

Sorry, not sure what you mean by a windows office prompt. If you can enter in your user name and password is should authenticate. At the site collection level of you site there are settings pertaining to the use of SharePoint designer on your site. Make sure the use of SharePoint designer is enabled.

Good luck...

I believe OP means he is getting this
instead of

I actually get the second box but it fails to authenticate my account as the above box is not an Office 365 login

I get the same thing sometimes and I click on cancel and it continues on and opens.

Give that try...