I will let others weigh in on the floor, but I think the gray floor might be a trendy mistake. I can not tell on my monitor how cool or warm it reads. You have a really sweet and in many ways timeless kitchen. I love it! It overall reads warm. It sounds like you might be struggling because you are trying to force cool tones and warm tones together.

For flooring, look for something that looks like natural toned wood - not gray wood. The natural tones are in - never really go out and will create a more timeless look. For walls, consider a cream, or light sage green with a gray undertone if you really want to bring gray in - that will read more warm.

The blue in this cottage works fine with the wood tones and creams and green - the chairs in you space are fine.

Creams / whites and warm tones:

Many of your colors all working together:
This wall paint might be a very light gray or white that leans gray - like Maritime White:

Assuming sink, window trim and chairs/table are white, you could do white subway tiles on the wall to the ceiling, maybe a tile "detail" of some kind over the cooking center.

Then add a Roman Shade over the window on a tension rod, in fabric to match the chair cushions. A nice complementary area rug, would help, too.