Could be too tight.

I use a 1/8" INOX chain... Not sure of the model or anything, but it's stiff as hell. No slippage or anything. It did make my drive chain louder, but I know it's not going to break or anything. I wouldn't run 3/32 on a fix - the chain is just too flimsy. I've stretched out too many chains to run another one. Give me a burly track chain any day.

I've never actually heard of anyone who's broken a well maintained chain, 1/8 or 3/32. There are 3/32 track setups. In short, I don't think you have much to fear from 3/32 unless you are the most gorilla rider ever. Having said that, I run 1/8 just because I want get my old skool on. I have two KMC chains, one is loud as all get out, the other is super quiet. I haven't looked closely to figure out why.

A couple of thoughts: does your chain have bushings? This will tend to make it louder than more typical bushingless chains. Also, a less-than-true chainline will make more noise than a straight chainline as the interiors of the plates rub against the gears.

the 'high-end' kmc z chains cost like 6 bucks by the way. they work fine. why spend more on a chain if you ride on te street?