Why is foam coming out of the kitchen drain while washing dishes?

I'd start by making sure you aren't just using too much soap in the dishwasher. More likely, the dishwasher is pumping water into the same waste pipe that the floor drain is connected to, and the pipe can't handle the water fast enough to keep the floor drain from backing up. I'd suggest two things:

First, check to make sure that the drain itself isn't running slow and start treating it with an enzyme drain cleaner. It probably wouldn't hurt to run a plumbing snake down the drain to make sure it isn't partially blocked.

Second, you can install a floor drain check valve for the drain in the kitchen floor to keep water from backing up through it. Even if you can resolve the issue by cleaning out the drain, this would probably be a good idea. You never know what else might back up through there some day.