Click File > Preferences > Keyboard Shortcuts:
Search for copyLinesDownAction or copyLinesUpAction in your keyboard shortcuts
Usually it is SHIFT+ALT + ↓
Update for Ubuntu:
It seems that Ubuntu is hiding that shortcut from being seen by VSCode (i.e. it uses it probably by its own). There is an issue about that on GitHub.
In order to work in Ubuntu you will have to define your own shortcut, e.g. to copy the line using ctrl+shift+alt+j and CTRL +SHIFT + ALT + k you could use a keybindings.json like this:
[
{ "key": "ctrl+shift+alt+j", "command": "editor.action.copyLinesDownAction",
"when": "editorTextFocus && !editorReadonly" },
{ "key": "ctrl+shift+alt+k", "command": "editor.action.copyLinesUpAction",
"when": "editorTextFocus && !editorReadonly" }
]