I think that furniture looks French Country and wouldn't be my choice with that kitchen. The rug is great though. Look for something more contemporary. It looks like the cabinets are Shaker? If so, that reinforces choosing furniture without all the round lines and ball details those white washed pieces have. I think the contrasting color is a good idea, it's the style that's wrong with those.

Stools yes, dining set gets lost with the rug pattern, you can add drastic vive color furniture and yet be elegant. Do not be afraid of turquoise, red engine colors.

I would say the style is not match but the color is ok. I mean you can go with different finish of wood in your dining set and it is not necessary to match them by color.
I say go with dark dining table and light dining chairs.The rug has light pattern on which makes the flow.

These selections are all from Restoration Hardware. Maybe something like these? It brings the dark and light together. I think any of these would work with the rug.

Don't go with the tufted chairs, to formal for the kitchen but these are in the right area

Barstools, can get wood and fabric in other options.

I think the counter stools will serve to unite both styles and wood colors. Perfect solution

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