VoiceAttack can send keypresses to any application, however that would mean switching focus to it, meaning your input would no longer be sent to any game you may be playing at the time until focus is switched back.
This "Stream Deck"(I'll assume you're referring to the Elgato product) likely uses some other means of interfacing, allowing it to send messages to the Twitch chat directly.
If you want to emulate the latter, you'd have to write a plugin or inline function through which VoiceAttack would communicate with Twitch using their API(there is
an unofficial C# library available).
For the bot you're using, it does appear to be possible to send commands or messages to that directly, as shown
here.
You could have VoiceAttack run curl with the required parameters.
Topic: How do I echo a voice command to Twitch chat? (Read 3218 times)
VoiceAttack User Forums