he commands your are looking for are editor.action.copyLinesDownAction and editor.action.copyLinesUpAction.
You can see the associated keybindings by picking: File > Preferences > Keyboard Shortcuts
Windows:
Shift+Alt+Down and Shift+Alt+Up
Mac:
Shift+Option+Down and Shift+OptionUp
Linux:
Ctrl+Shift+Alt+Down and Ctrl+Shift+Alt+Up
(Might need to use numpad Down and Up for Linux)
Furthermore, commands editor.action.moveLinesUpAction and editor.action.moveLinesDownAction are the ones to move lines and they are bound to Alt+Down and Alt+Up on Windows and Mac and Ctrl+Down and Ctrl+Up on Linux.