I do not have personal experience, but I can provide some recommendations on how to remove stains from a slate kitchen:

1. Identify the type of stain: grease, oil, wine, rust, ink or food particle.
2. Prepare a solution of hot water, mild detergent, and white vinegar.
3. Soak a soft cloth in the solution and apply it to the stained area.
4. Let the solution sit for a few minutes.
5. Gently wipe the area with a soft-bristled brush.
6. Rinse the area with clean water.
7. Blot the area dry with a clean dry cloth.
8. Repeat the process if the stain is not completely removed.

It is important to avoid using abrasive cleaners or scrubbers that can scratch the slate surface.