How can I tell when looking at a pet's profile if the genes it has are carried?

By the color of the words.

Blue: a visible trait (such as AA)
Purple: a visible trait with a hidden underneath (such as AB)
Green: a carried trait (such as NA)

keep in mind that the pet nead to be tested for you to see carried and ressessive traits unless they are generated or starter pets. ^-^

Thank you so much! :)

if you want specific traits for pets i likely have it for sale and i can lower the price for you so that you can have pets with good traits starting out :)

I looked through your pets for sale, and thank you for the kind offer! But I'm really for Zolnixis I can breed with carried or hidden traits, and you don't seem to have any of those. Again, thank you so much! I might dabble in other Sylestian species after I get a good start up with Zolnixis. I could possibly go looking later on, but for now I'll stick to one to get a basic understanding :)

not sure if this will be helpful at all, but we have a post that breaks down trait inheritance

Yes, that did seem to help me a bit. I can now also refer back to a source if needed. Thank you!

New question: where can I get Genetic Test Kits? I can't seem to find them anywhere. Sorry if it's blaringly obvious :')

it's a perfectly reasonable question and the answer is: other than the newbie kit and maybe december advent calendar? You can't get 1-use ones.
Way back when, there was a Wheel at fests and 1-use scanners and testers were something you would commonly get from the 'consolation prize' section, but the Wheels were retired and now there's no real way to restock the things.
Maybe someday there will be a new way to get them (honestly I feel like they should be available to buy from one of the towns, but nope)

Best plan: Save up the diamonds needed (or the gold to be able to buy the diamonds needed from the currency exchange), then buy the Exceptional Scanner and the Exceptional Test kit (in that order- better to get the scanner first by far)

If you need a pet you own genetested, there are people with threads in the Groups, Guilds, Clubs, and Services subforum who will test people's pets for free
(hence why I suggest buying the Exceptional Scanner first- other people can't scan wild pets for you)

It's cheaper to buy them when there's a diamond sale or during the black friday sale.