If you look at your second picture, you can see that the grain of the floor and the grain of the cabinet are already very compatible so IMO the flow already exists. If it were me, I'd want a light porcelian tile floor in the kitchen.

Light meaning white or a creme color?

I wouldn't go stark white; a creme color or even creme with some beige marbeling should work.

I am not a professional at all. However, I have done 3 additions and in the process of my 2nd remodel all on the same house.

So in my amateur experience, I think there is way too much grain appearance in the cabinets and the wood floors for both to exist in the same room.

I would suggest,
1: a rug with some color. Perhaps a runner.

2: if you brought the wood floor into the kitchen, paint the cabinets. However, I don't like the cabinets painted with grain. Depending on your budget, new light cabinet doors would look awesome and make the whole house look less chopped up.

18 inch tiles maybe a lighter color the space is dark

I build custom homes for a living. It's my opinion the wood grains are not compatible because they are not the same color of stain. Clearly the adjacent floor is hardwood oak with medium stain and the cabinets appear to be stained a chestnut colored stain. Your kitchen floor, counter top and back-splash need to compliment the cabinets. There is no need to paint the cabinets. You need to replace the existing red tile floor with, as mentioned by "olldbobbi", a beige, marbeling tile. I suggest using a larger size tile, possibly 20x20. The counter top and back-splash could be renovated in similar beige tones and would make a striking improvement.

I'm a woodworker, and wood is my friend, but in my opinion its too much. Large tiles 12 x 24, 18" x 18", 16" x 16" or another combination etc... Larger than 12" x 12". Color on the lighter side but not white

I will tell you what I have done in my kitchen :))
I went to the store got a small can of paint and painted the grout . A bit of kneeling down but I done it !

I like the runner idea.... easy to change out and adds a pop of color!

Your current floor seems very nice, you just need to transition to the wood flooring. I agree that the right runner would compliment the space and tie the wood and tile together.