No vinyl pank will look like your wood so just match the wood . Wood floors have been in kitchens for a very long time and have stood up very well.. IMO if farmhouse it he look you are after change the carpet for wood too. The more cohesive the flooring the better the spaces will look and the whole place will feel larger .

Vinyl will not be as warm as wood, but it will not be as cold as tile. Vinyl is more dynamic than anyone likes to talk about. A house that experiences large temperature swings and humidity swings can be problematic with vinyl. Vinyl can, and will warp, in direct sunlight (with older windows with zero UV filters). In a 4 season situation, I prefer a high-quality laminate with cork underlay for thermal and acoustic insulation. It costs the same as a medium grade vinyl. Vinyl does NOT like underpad (which includes the incorporated underpad on the planks). Which means it will sit directly on the concrete AND you will have a large floor height variation. Tiles often sit 3/4" high (18mm). Some thin vinyl = 5mm. That means you will have a 1/2" drop between the tile and the vinyl. Laminate accepts 6mm cork any day. Your 12mm laminate (1/2") and 6mm (1/4") cork underlay add up to 18mm = 3/4". You get an even transition between the tile and the laminate....vinyl, not so much.

Here's my take. As a flooring expert (I'm a cork gal so I have to know everything about everything else as well) I would say you need to choose the LESSER of the two evils. I know a very good laminate ($3-$7/sf out of Europe) will out perform the SAME price LVP (anything under $3/sf is to be avoided at all costs). If you want to run an inappropriate material in your kitchen, you are welcome to do so. My suggestion is this: purchase DOUBLE the kitchen square footage. That should give you 50sf-200sf of extra (on top of your extra). Why? So that you can achieve a FULL floor replacement in the kitchen at some time later in your life. It sounds more expensive than it is. You simply store these boxes (flat and off of concrete slabs) until you need them. It is MUCH MORE expensive to have to redo EVERYTHING in 4 years (laminate and vinyl = 18 months on the shelf and then they disappear forever...never to be seen from again) than it is to replace the kitchen with the flooring you already have. Now...vinyl HATES heat. Really really hates heat. A pool of sunlight = IR (infrared = heat producing rays). Vinyl HATES UV rays (the things that fade vinyl). Windows that have a high UV rating also have high IR ratings (same film filters both). How do you know if you have a high or low uv rating on the windows? Easy. Simply put down an outdoor thermometer on the floor where the sunlight pools. Leave it there. Check on the temperature after an hour or so. And then every hour after that. If, at ANY TIME, the temp reads ABOVE 85 F (yes...it is THAT LOW for vinyl) then you cannot use vinyl. It is simple as that. To get vinyl in that area, you need to do SOOOO many things that you would be sick if I laid it out for you. A laminate floor is fade resistant. Much more so than most vinyls. It also doesn't care about extreme heat. The one thing laminate hates = water. If you work with a HIGH END European Laminate (Lico out of Switzerland is one...amazing stuff...it's better than their watches...not kidding) you can get quite a bit of water-resistance out of the fibre board. Just remember to budget for 2x the kitchen square footage. You will be super happy you did. Remember: the MOST damage comes from FRIDGES with water/ice production. The other most damaging appliance = dishwasher. The steam from a dishwasher is enough to warp a $0.79/sf asian import laminate. And it will happen within 2 years.

The fireplace has already been white washed and looks nice. Solid color paint doesnt look nearly as nice as the white wash you already have. The mantle appears to be black, and you seem to have other black accessories. I would leave that also.