No fake wood next to real wood -- the contrast will be terrible. Get a tile-look vinyl if that's the direction to go.

My kitchen is relatively small, and it sits between the dining room and family room, both of which have hardwood. I’m using hardwood floors in my kitchen. I put a beautiful faux hardwood ceramic tile under the cabinet run with my refrigerator (water line) and will do the same under the cabinet run that will hold my sink, so that if anything leaks it won’t ruin my floors.

i know you don’t want hardwood floors in your kitchen, but I think you know that that’s what will look the best. If you want option other than vinyl, you can always go for linoleum (marmoleum) in a wood look or solid color that blends well with your medium brown.

no to fake wood, no matter what material it is printed on. it will look terrible where it meets the real wood.

We put cork flooring in the kitchen of our previous home that had oak flooring throughout the rest of the house. The kitchen cabinets were white and we chose a cork that was similar in color to the oak floors. It looked good with the similar colors, but distinctly different materials. And it was so comfortable to stand on! The only issue we had with the cork is that it faded in one spot that got direct sunlight. I would use cork or linoleum/Marmoleum in the kitchen of a traditional home with wood floors.