Kentucky Case law has found balisongs to be deadly weapons and thus not ordinary pocket knives or hunting knives. Even without the case law, I can tell you that no officer or court would consider them to me "ordinary pocket knives." They are almost always interpreted as weapons, and you'd never convince an officer that you were carrying it for utility.
So no, it is not legal to carrying a balisong in KY.
And just a bit of helpful advice:
Since you're using the word "pack" to describe carrying a knife, it sounds a lot like you fully intend to carry one as a weapon. I'll leave aside the debate about how well knives can function in a self-defense role, but I will tell you that carrying a knife for that purpose can get you in a world of trouble. If you tell an officer you're carrying a knife for self-defense, you'll probably face weapons charges. If you carry a knife that looks like it was designed as a weapon, you'll probably get charged for carrying a deadly weapon under KY law (they've got the Case law to back it up). If you ever do use a knife in self-defense, you'll become the defendant and have to prove beyond reasonable doubt that your actions were justified. Plenty of times people have stabbed someone in so-called self-defense and the original victim ended up with a prison sentence. Even just pulling out a knife to deter an attack (often called "brandishing") can and probably will get you in trouble.
Reading your posts here, you seem kind of young and/or immature. Sorry if that seems a bit blunt, but I'm trying to keep you out of trouble here. If you're that concerned about your personal safety, get some pepper spray. Police and courts will be a lot more understanding about that. If just think it sounds cool to carry a balisong around in your pocket and/or you're harboring fantasies of pulling it on some punk that tries to mug or attack you, then you'll need to adjust that way of thinking.
Again, I'm sorry if I'm mistaken in my interpretation of your intentions, but your desire to "pack" a balisong really makes it seem like you're just interested in carrying a weapon.