If you can't get it stirred up enough to get the consistency of regular paint, don't fee bad as it's hard to do with Kilz. You can take it back to where you bought it if they have a paint mixing department and they will put it in the mixer unit and give it a good 'shake' that should do it but use it within a few days so it doesn't separate again. You can actually take it anywhere with a shake box to mix and they will do this for you.
are you using a brush or a mop?
I stirred the primer for a few minutes and poured some of it into a pan. When I spread it across the wall, it drips down the wall like water. Is this supposed to happen, or it supposed to be thicker like paint?