I'm just gonna say that Flight Rising is
not seem similar to CS at all, I'm sorry lol - I see a lot of people say that, but I think the two are VERY different in how they function. I say this as someone who loves CS and has given FR a lot of chances and it doesn't hold up to what I personally look for in site-games at all. Just me ranting; there's way too much to get into to the point where I don't consider it new-player friendly, and it sucks that I don't enjoy it because I LOVE dragons and I really want to love this game as well, but it's just missing so much of what I want while having too much of what I don't like. Alright, rant over.
If you're looking for another site that lets you "adopt" pets and they grow on their own, maybe try something like
Gothicat World (which
is, by default, in French, but your browser should be able to translate it for you). It has the same "adopt x" feature and they release a new set on a regular basis, just like CS does. (Part of me really wants to give an honorable mention to
Edlemore since it was probably the closest thing to CS you'll find, but they've been inactive since 2017 :C)
Also
Dappervolk, but they seem super money-driven imo. I think the effort comes in finding incubatable items, though once you get a system going (hatching the turnips, using potatoes to get better items), it's not too terrible. They also don't release regular sets of pets (in the same way CS does). I know of
Goatlings, but it's been SO long since I played, that I couldn't tell you much about it.
I think click-adopts in general kind of function similarly to CS in that you adopt random "pets" and they, for the most part, grow on their own. For these, I can suggest
Dragon Cave,
Final Outpost, MagiStream, and a few others that circulate the web. I can't link to MagiStream because it seems like they're doing maintenance and have taken the site down temporarily? Also DragCave is lowkey my favorite thing rn ngl (~
my scroll~)
However, if you
are looking for something that requires some effort into making your adopts/animals/whatevers grow,
Flight Rising fits into this category, along with
Wolvden/
Lioden,
Herd of Hounds, technically
Furry Paws (if you're into dogs, genetics, and competing), and honestly I think the vast majority of other online games like this. Someone made a list of sites (some may be inactive)
here and a lot of people try to make their own pet-collecting games and advertise them in the "other websites" forum section!