We have a 1930's farm house & need to replace the flooring in the kitchen. However, the floor is uneven. Previous owners added on part of the kitchen and now there is unevenness in the floor where the addition is slightly lower than the original section. I would prefer not to put carpet in again as I know most buyers won't want carpet in their kitchen. We're fearful though that vinyl would crack at the seam. Any suggestions on how to deal with this?
Thank you.

The first step is to determine that you do not have any settling or movement in the existing flooring - both in the new and older sections.

After that, you can level the floors by using a leveling compound, shims, layers of vinyl or 30# felt and then cover with a skin of plywood. Then, you can install your finished floor on top of that. Biggest down-side is that you will be raising the floor somewhat.

If you want to avoid raising the floor, then you are in for a larger project of removing all subflooring down to the joist level, leveling or sistering the joists to get everything even and then adding a new subfloor over the entire area.

Once the floor is skimmed smooth with the cement underlayment you can DECOUPAGE the surface to look like stone. See my How-to on Decoupage Floors on YouTube or my website, DecoupageFloors.com
The flexible surface will work just fine over your uneven surface, create virtually no transition change, height-wise, and be a beautiful, custom colored flooring you can do yourself! It's easy once you know my technique and tons better than any of the "paper bag" techniques. Mine is a professional-quality, smooth and durable floor. Almost forgot, my decoupage floors stay flexible to move with the house shifts.