The application of a sealant such as polyurethane, varnish, or wax will make the surface of your kitchen cork tiles as impervious as any natural material can get. Regular re-application will ensure that the cork is protected against stains and spills, while also creating a seal over it that will help to reduce some of the scuffing damage that can occur.
When spills do happen they should be wiped up immediately. Never allow liquid to rest on the surface of a cork tile floor, as it can penetrate the material over time and cause damage from the bottom up.
Basic maintenance will require you to vacuum or sweep a cork kitchen floor every few days. It is important to keep the floor free of dirt particles which can scrape the surface, biting through the sealant, and damaging the tile. The material can also be dry mopped. Never soak a cork floor in water in order to clean it.
There are a variety of cleaning agents that are made specifically for use with cork flooring tiles. In the case of set in stains, the individual tile can be removed, replaced, and then sealed to match the rest of the application. Cork kitchen floors can also be refinished several times depending on the thickness of the tiles used.
Aside from basic spills, water accidents do sometimes occur in the kitchen. Floods due to faulty dishwashing equipment or leaking pipes beneath a sink can cause stains and warping to occur in tiles. Regular re-application of the sealing agent can provide some protection against these disasters.