Stripping zinc electroplating with phosphoric acid - hydrogen danger?

I'll start by saying that I'm not a chemist, more of an artist. I'm stripping zinc electroplating from some regular hex bolts, nuts, and washers. I'm using a product called Ospho. It's basically phosphoric acid with a surfactant and a couple other additions, from what I understand.

I've read that zinc and phosphoric acid react to produce zinc phosphate and hydrogen gas.

My unknown is whether this hydrogen gas is emitted in great enough quantities to be dangerous / explosive when this reaction is carried out indoors. I don't know how much zinc is being reacted, but electroplating leaves an extremely thin coating and I'm talking about small quantities of fasteners.

Yes, mineral acids like $\ce{H3PO4}$ react with electropositive metals like zinc to produce dihydrogen gas ($\ce{H2}$).
The quantities generated of course depend on how much metal is being dissolved that way. About $65\ \mathrm{g}$ of zinc would produce about $44.8\ \mathrm{L}$ of hydrogen (in Standard conditions).
Yep, there's no danger of any problem, provided there are no flames in the immediate vicinity of the reaction. $\ce{H2}$ is lighter than air, so it disperses itself and doesn't pool like most flammable gases.
If you were dissolving zinc powder, then you'd have to know that most zinc powder contains zinc sulfide contaminants, leading to toxic $\ce{H2S}$ emissions. But that's not an issue for you.