I don't think the LabVIEW sound API supports multiple audio streams (or buffers, I've forgotten what the correct term is). Can you get away with just adding the two waveforms before passing to the sound output write VI?
I did have one application where I needed to be able to play multiple .WAV files at the same time (sound effects for a game). What I ended up doing was using the .NET DirectSound API with a lightweight wrapper DLL. It only works with .WAV files but if it would help I could dig it up and post it.
I'm hoping it's fairly self explanitory. This is how you'd use it:
I've also just realized my example doesn't explicitly close the .NET reference. You should probably do this, like so:
The game I created this for was the Angry Eagles demo we showed at NIWeek. You can grab the source for the game here to see it used in context - https://decibel.ni.com/content/docs/DOC-17552 (or if you use the actor framework you can just grab the SoundManager actor and drop it in).