How can I stop the water from pouring out from under the sink and back in the wall? It seems like it is coming from the vent pipe back in the wall, but I can not see it for sure. Every time I turn on the faucet water gushes down the pipe and starts to flood under the sink and the kitchen floor. I've already used drano foam thinking it could be a clog in the pipe, but it was no help. I can't run water in my kitchen or wash my dishes, what can I do?

Sounds like you have a blocked drain and a poor connection in the drain pipe.
To make sure that it is coming from the drain pipe put the stopper in the sink drain and run some water in the sink. Then look for water under the sink. If no water pull the plug and again look for water.

If water is coming from a supply pipe it will leak while you are running water. If it is coming from drain pipe it will leak while sink is draining.