Waht are thr red wood pics. IMO flooring should all match so whatever you have in the rest of the main living space is what should be in the kitchen . If that is not possible then IMO a completely differnt material for the kitchen Pretty sure you could do unfinished for the kitchen and have it stained to match the other flooring that would be my first choice. From what I see you already have wood floor in the kitchen so not sure exactly what you are asking.

What’s wrong with the wood floor you have now? And, why the different (darker) wood floor in the adjoining room?

Quite frankly, it’s your backsplash that need changing. Yowza!

I agree with the above. First of all, you shouldn't be adding yet another kind of flooring in your kitchen, different than your dining room or foyer. No matter what, it is going to end up looking haphazard and not intentional. While we certainly all don't have the funds or the ability (because of the disruption) to remodel every room in our houses at the same time, at the end you should end up with a coherent result. If you like the floor in your dining room, you should strip and stain the existing floor in your kitchen to look the same as that. If you don't want wood in your kitchen anymore you should be looking at porcelain tile or LVT - tile look. Putting fake wood look next to real wood is never a good look. Also, any tile look should coordinate with your foyer, which is I assume is the multi-colored slate shown in the picture. Pick one of the colors of slate for the kitchen.

I will also warn you that if you do decide to put another layer of flooring down on top of what is already there you are in danger of trapping your dishwasher and possibly also your frig such that they can't be removed to be serviced or replaced. Flooring guys aren't thinking about that, nor do they care since it's not their problem. I speak from experience. :-) This also happened to a friend of mine.

We need to replace the kitchen flooring because there are areas that are damaged. We cannot refinish the existing wood. And we are not adding a new layer of floor, we are removing what is currently here and replacing it.  

It is not an option to use the same flooring from the living room in the kitchen. 

And curious, @darbuka, what is wrong with the backsplash?

Real wood, stained to match the wood flooring that abuts the kitchen. If you can’t do that, slate or large format tile. Don’t do wood imitation anything.

Heather, the vertical backsplash is too busy, very haphazzard looking, and quite dated.

As for the floor, like @Lynzy suggested, get real wood and have it stained to match the abutting wood floor.

I honestly don't like either of your samples - the one is much too red, and the other too light. Is there an option that would be more similar to the color of your living room floor? If not, I'd go with a slate that matches one of the colors in your entryway.

I’d go with a porcelain tile in a kitchen. Can you replace the tile in the foyer too so it would match the kitchen tile if that is what you choose to do?