If the bike has been sitting any length of time, you will need to clean the carburetors. The carbs on the 440 are fairly simple. You most likely have a float needle that is not sealing well against the needle seat. When you put the petcock on Prime, the fuel is designed to flow directly from the tank, uninterrupted. If there is nothing stopping it (like the float needles) it will overflow the carburetors, which is what is happening.
The prime position is intended to be used only to fill the carbs. When the petcock is in the On or Reserve position, the bike needs to be running or at least turning over for fuel to flow. A running bike creates vacuum and there is a vacuum line running from the carbs to the petcock. This vacuum turns the petcock on by opening a small valve. If you tried to fill the carbs with the petcock in the On position, it would need to turn over for a long time in order to fill the carbs. The Prime setting is a shortcut and fills them quickly.
There is another possible thing that might be going on: the overflow tubes inside the carbs might have a crack in them causing them to dump fuel before they are actually too full. I have seen it happen on older bikes. They can be closed with solder. Do not try to put any type of glue, sealant, or adhesive on them. It will not work.
The KZ440 is a nice little bike. They are reliable, simple to work on and the engine is pretty bulletproof. Download a manual. Read it. Understand it.