I'm going to begin a Vulnyx project soon, but don't know what accent colors are. Do the accent colors visibly show up on the pet, or does it only show up on offspring?

There are two accent colors. Accent color one is primarily used for the genes while accent color two is primarily used for the mutations. The accent colors are used as secondary or third colors on the genes.

If you want to know more about the generator, I recommend this guide for help.

I'll also note, there are a lot of species that barely use accent colours- this is because they've only relatively recently been added (ac1 was implemented functionally on 25th January, 2017 with the puffadore revamp, ac2 was created 13th August, 2017 with the lune revamp)
"2017 is not recent?" would be an undersandable question here, so we will pretend it was asked, and the answer is: maybe, but we've only had one species revamp since then (lupora) and one new species added (ferrikki), so lune/lup/ferrikki are the only ones with full ac integration.
For all other species, the accent colours are only integrated into new traits that they've gotten since then, rather than having them cleanly integrated across all traits (and at this time nyte, fae, and bulb use only ac2, and only in the spring blossoms mut, but can be expected to integrate ac1 and 2 in the future once they've had their revamp. Several other species are set to get lesser revamps than those three, at which point they will likely also integrate more of the accent colours into their traits)

(for vulnyx, the only traits the acs are used in is ac2 in M3 ram horns and M3 spring blossoms)