Lowes has Smartcore Naturals hardwood plank flooring that is spc with real wood wear layer instead of vinyl for $4.19. Same click install. Free samples to bring home.

I’m not an expert but common sense tells me it would be best to lay new flooring over a smooth, fresh and clean surface. A surface that’s the same everywhere. I can’t imagine laying anything over old carpet.

You cannot lay vinyl over tile with grout lines - the grout lines will telegraph through. Vinyl needs a smooth surface, which means the installers will want to lay a layer of plywood down first. Plus, if you add those layers on top, the installers will have to cut the door molding shorter & probably cut the doors too. That means that if in the future you have to change flooring again, when you will definitely have to take out the extra layers, the door molding will have to be replaced or repaired.

So, I say pull out the current flooring, down to the subfloor. Do it right, once.

If you lay it on top you will also have issues with your appliances since the curb will too high to say pull out the dishwasher or stove.

Another vote for hardwood, it will look lovely with your kitchen! :)