Is this correct that it's an open concept that shows grey sofa and 3 white tables? Walls everywhere: greige?

You said color palette below, and I'm assuming you meant the flower and 5 colors?

I'm thinking a light wood like color of counter/ I guess that's photo of floor...softer to blend with your colors.

The coral-salmon-pink of your palette could be in rug, etc. but deeper in modern pattern, etc... to tie in with warm cherry cabinets.

everdebz, yes you got it right, I think when I uploaded the pictures my cursor wasn't at the bottom and the pictures were clipped out of order. Thank you for your imput.

Cynthia, thank you for your idea I like it a lot! :) I failed to mention my appliances are black.

Well that does tip a balance toward darker then... but if kitchen area is on small side I wouldn't add a dark set ....

So, if I'm getting your ideas right, it should be something like these? Staying on the small side since I lack space of course

I would go dark wood and white table with bright chairs to complete your colour scheme, fun with a pop of colour, great for children. Buy the table and source second hand shop for chairs to paint

I'd paint those cherry cabinets and then get the table you love.