I haven't jumped into the KP-9 yet myself, but I had a wild hair and looked into all this, primarily from a SBR perspective but braces share the mounting systems.
The KP-9 uses a 5.5mm AK folding stock trunnion with a locking post on the front left of the receiver.
So what options does this leave us with? The most basic are Vityaz-style
triangle stocks and
triangle braces. These mount directly to the 5.5mm trunnion, fold to the left, and lock onto the post.
You can go more tacticool if you want, but you will give up locking the stock when folded, unless your stock/brace option has a tensioned hinge in it. Anyway, the first option is the
RSA-5.5 from JMac Customs. That gives you a 1913 stock rail and all the options there. Sig MCX/MPX stocks and braces, the
SB Tactical 1913 brace, etc. There's also a
5.5mm adapter for AR stock tubes. Put on your choice of receiver tube or pistol extension with the appropriate stock or brace, and you're all set.
Hopefully that helps. I'd personally go the KP-9 route, SBR it, then put on the classic triangle stock. If the world doesn't end this year, I'll consider it.