What Type of Gas Would Vinegar and Epsom Salt Create Under Electrolysis?
You're most likely forming $\ce{H2}$ gas at the part.

If you're plating anywhere above about $2~\mathrm V$, that is probably sufficient overpotential to cause part of the passed current to go toward electrolysis of water.

There is negligible toxicity hazard to inhaling the small amounts of hydrogen that would be generated from an electrolytic cell on this scale.

There's a small ignition hazard if anything sparks near electrolyte of the plating cell as it's operating, but as long as you're not running it inside a tightly closed, small space you should have nothing to worry about with how small the cell is.