So in my head canon a kirin is actually a cross between a dragon and a pony (male dragon x female pony. Kirin produce live offspring. It’s also a dominant trait so even in a kirin x pony pairing you will still end up with kirin traits.). A group of flying dragons may be considered a flight, and a group of non-flying dragons is a weyr. So I'm going to refer to a group of kirin as a weyr.
One of the things that bothered me in the show was the lack of sexual dimorphism. That doesn’t necessarily have to be a trait of every species, but if it was deliberately left out there was no explanation. So I added some. The males are larger, and as opposed to females (who have smooth scales along their back and head), they have a set of spines along their face, head, and back. Their horn(s) is also larger and a cooler brown/black (as opposed to the warm brownish burgundy shown in females), and instead of a single horn that may or may not branch off they actually have the potential to grow 1-3 separate horns. These horns are all connected to the same part of the nervous system, allowing them to work in unison (so, no, each of their horns cannot do separate things) and losing or damaging one will not necessarily impact magic ability. The number of horns a male will grow is pre-determined. A male will also have substantially more floof than a female that will run along their entire underside, whereas a female may only have a traditional kirin mane. While not necessarily the rule, it’s not uncommon to see the males coming in more muted shades than the females.
So yeah! Those are just some of my ideas. Let me know what you think.