Muted green sounds lovely. I see a brick fireplace in the mirror. If that is in the living room, I think your biggest task will be finding the right green to compliment the brick. The tiles and rugs seem very neutral and like they will go with many colors. Can you include more pics of your living room?

The couch is going to be replaced so mainly trying to match with the chairs/brick as well in this room

I wouldn't worry about green clashing with the white and just find a green that works well with your room’s components, like sage.

You could also just paint the wall with fireplace and use a darker shade, such as olive which has an earthy feel (as does sage).

I think a green like this would be great

The living room will look fine painted in most soft muted greens.

Your kitchen will look fine as a white on white kitchen.

They already have different floorings and I am think you are correct to worry about how you are going to make the two feel harmonious and not like the kitchen belonged to another home and was just plopped on the back of this house.

Even now it looks like you selected a cooler white for the kitchen than the white in the living room and dining room. (Could just be the picture).

Whatever color you pick for the living room/dining room you should add some of that color in various shades to the kitchen so the two rooms feel like there is some connection.

Look at Benjamin Moore Quiet Moments