No, I've never heard of slings being used by prisoners. It's a ranged weapon that needs room to swing, so most indoor use would be difficult, and use on a prison yard would probably not be much better. There's also the difficulty of finding ammo. Anything that could be slung can be thrown, so the powers that be would be trying to limit unsupervised access.

I spent years working with convicted gangbangers and they can be pretty innovative when they want to be. That being said a sling requires more than that. You need a serious amount of patience and skill to really make it useful. I can say I personally would not have the guts to sling at someone in the prison yard. If you were to miss the intended target altogether or hit another inmate the end result would be you dying a horrible death.  A shiv would be much more effective.

yes glands propelled by gun powder are more effective sadly