Right now, from what I've been told, you just have to make a new account on the other instance. Some federated services allow "account migration", but kbin doesn't have that functionality yet.
The "correct" answer currently would be to copy the link to the instance you have an account with if you want to interact with it.
I would expect that, as federated services get more traction and are inhabited by a larger proportion of non-hobbyists, these clunky areas will get more work. The majority of people using these services now are hobbyists and they're willing to accept the jank for something that they want. Most "normal" people wouldn't, but there haven't been very many "normal" people in federated spaces yet - in no small part because of the jank being a barrier to entry.
There isn't a native mobile app, but this website is what's known as a "progressive web application". This means that you can just add it directly to your home screen and it will act app-like. See this thread for exact iOS instructions. Android is similar but does depend on which browser you're using.
kbin.social is getting the hug of death right now, consider signing up for another instance
Hey Reddit refugees! You may have noticed that kbin.social is taking forever to load because of all of the traffic it's getting....
Reddit CEO: We're Sticking With API Changes, Despite Subreddits Going Dark (www.pcmag.com)
/kbin Issues (codeberg.org)