Rubber so does NOT mix with kitchen grease!

This is the sort of thing they use in restaurants and fast food joints. But it's usually in the form of open celled floor mats that can easily be removed and the floor can be cleaned. I'm not sure why anyone would want to use it their home, unless you run a catering business.

Maybe you could buy it by the roll and cut and lay it out as you see fit.

Here's a place I found when just googling your question.

http://www.rubbercal.com/

There are some DEVASTATINGLY expensive "gym" floors (commercial/light industrial) rubber floors. They have a "finish" on them that is kinda like vinyl...but not quite. They "look" like wood, can be 3mm - 8mm thick and are often used as school gym floors. They take a VERY expensive form of install, and have some weird issues with edges and seams (the tolerance for rubber flooring like this is VERY weird...and often leaves a 1mm "lip" where two pieces meet). Some installers charge $6-$7/sf + cost of seams + cost of tools (many tools are damaged during cutting/trimming). It can work out to be almost $10/sf for the install. Then there is the cost of materials - which are not cheap.

That's the good news. The bad news is trying to find this type of floor with the type of "finish" (not the open celled rubber mats that are thrown away every year because of the crud embedded into them).

If you want a tough floor that is easy on the legs: sheet linoleum or cork flooring. Both can handle kitchen life.