What's the shortcut to close vscode's message box?

esc should dismiss all visible messages.

You can also configure a custom keybinding for the leaveEditorMessage command (or workbench.action.closeMessages on older VS Code versions). Here's the default keybinding:

{
  "key": "escape",
  "command": "leaveEditorMessage",
  "when": "messageVisible"
}

Updated, as of Jan 2020:

{
    "key": "shift+escape",
    "command": "notifications.clearAll"
}