From what I can find, Razer doesn't offer a macro-related API, and Synapse doesn't appear to have command line arguments for changing profiles.
I'd say you have two options(provided you can't find a method to set profiles programmatically):
Have VoiceAttack open the Razer Synapse software, and use mouse and/or keyboard actions to switch profiles; This will require tabbing out of the game, and waiting for the window to pop up, not ideal at all.
Alternatively, you could make use of the application-linked automatic profile switching normally used to switch to a profile when a game starts, for example, by having VoiceAttack start and stop dummy executables(which would just sit idle in the background) linked to profiles, to make Synapse auto-switch to different profiles at will.
E.G. you have "dummy1.exe" linked to "Profile1", so you speak "switch to profile one", whereupon VoiceAttack starts "dummy1.exe", and Synapse switches to "Profile1". Then, you speak "switch to profile two"; VoiceAttack stops "dummy1.exe" and starts "dummy2.exe", making Synapse switch to "Profile2", etc..