The shortcuts I use in Visual Studio for multiline (aka box) select are Shift + Alt + up/down/left/right
To create this in Visual Studio Code you can add these keybindings to the keybindings.json file (menu File → Preferences → Keyboard shortcuts).
{ "key": "shift+alt+down", "command": "editor.action.insertCursorBelow",
"when": "editorTextFocus" },
{ "key": "shift+alt+up", "command": "editor.action.insertCursorAbove",
"when": "editorTextFocus" },
{ "key": "shift+alt+right", "command": "cursorRightSelect",
"when": "editorTextFocus" },
{ "key": "shift+alt+left", "command": "cursorLeftSelect",
"when": "editorTextFocus" }