What do I need to do to be able to use keyboard combinations, instead of Touch Bar clicks?
Keyboard shortcuts can be found in System preferences -> Keyboard -> Shortcuts. You can set any shortcuts to any keyboard combinations you'd like. The default for voiceover is Command + F5, which can be changed.

The Touch Bar can also be set to only display the Function Keys, instead of app specific context keys. While you won't be able to feel the position of them, they will remain there when any app is open, acting like a standard keyboard rather than the Touch Bar.