simple question, how stiff do you think legs should be while boxing (so the knee isn't bouncing everywhere) ? Any help is appreciated

I wouldnt even think about that, you got enough to think about in there.

Naturally your leg muscles shouldnt let your knees cap down when you bend slightly to sit on a punch more or move slightly up and down it will be all happening natural and automatic.

But if your talking bout moving around on rigid legs forget it.

You should all be doing stretches ,the splits, low squats ,warm ups of every lower joint by revolving them fast, as well as hips, back stretches etc etc so that you are more nimble more flexible because the path from your big toe right through you to your wrist generates power and speed.

But have you got knee trouble?