It is possible to assign a keyboard shortcut to any action on the PDF menu of the standard MacOS Print dialog.
Add a shortcut for Save PDF to DEVONthink 3 by using System Preferences → Keyboard → App Shortcuts → add Save PDF to DEVONthink 3 (CMD+P)
In conjunction with the MacOS command-p shortcut to invoke printing, you can have a two-shortcut routine to quickly get a PDF into DEVONthink.
exmple:
Keyboard Maestro → Chrome
Keyboard Maestro → Safari