Hmm, I don't know that much about growing, but I know a bit about chemistry.

Vinegar is weak acetic acid solution. Baking Soda is Sodium Bicarbonate (NaHCO3)

Acetic Acid + Sodium Bicarbonate -> Water + Sodium Acetate + CO2.

Water is obviously harmless.
Vinegar is harmless.
Baking Soda is harmless.
Sodium Acetate is a harmless salt. It's used in chemical handwarmers and stuff, nothing to worry about.
CO2 is what you want.

The Calculations for how much Baking Soda you have to decompose to make the desired amount of CO2 are relatively simple