Discord responds to hotkey Ctrl + K which brings up a dialog to go to a specific channel. Set up your VA command to send Ctrl + K to the Discord window, Quick Input the name of your target channel, send the Enter key, then send your text to Discord. Optionally Ctrl+K to go back to your previous channel if you wish.
Doing all this will probably cause ED to lose focus, so remember to have your command set your active window back to the ED client at the end.