Those choke flaps are a common failure on kz's, my buddy's 550 is missing three of them. It is usually the spring that breaks and then you lose the flapper. If you didn't find the parts in the pod they are in your exhaust by now, almost guaranteed.
There is no way they are just flopping around in the cylinder. Pull the plug, make sure it isn't bent closed and hope for the best. Those little parts won't blow an engine, they just get worked through, maybe scar some surfaces along the way.
The uncontrollable high rev could be from the flappers. You have essentially lost part of your choke. With that one down it is only like half a choke. Yeah if you measure volume technically it's different, yadda, yadda but just kinda think of that cylinder as only being half choked now because of the big hole there now. Are any more of the flappers missing?
Usually two of them is alright for cold weather, any more than that missing and you may have issues starting it on a real cold day, it won't choke enough. If one broke, the others may not be far along, who knows. It doesn't seem to be a common failure on our bikes tho, could have been a PO 'fixing' it