The sustainable building/interior product sector is still in the infancy stage, but green flooring options are numerous.
There are many kinds of FSC-certified wood floors that are either solid or engineered. Reclaimed wood floors are beautifully unique. Stone can be a gorgeous choice. Just make sure that it is salvaged or locally finished and quarried. Another great choice is post-consumer recycled terrazzo. Linoleum (not vinyl), cork, recycled-content tile, and bamboo have environmentally friendly attributes but as with all green products there are pluses and minuses. We must research to determine all the pros and cons and ask the necessary questions of the manufacturer.
Concrete flooring, environmentally speaking, does have its drawbacks. The production of Portland cement is energy intensive and adds to carbon emissions. One solution is to add slag or flyash. There is some controversy over adding flyash (a waste byproduct) into ready mixes due to possible toxic offgassing, although some consider concrete to be inert and safe once is has hardened.
Whatever choice you make, keep in mind that you may need to stand on this floor a lot, as it takes time to cook a good meal and clean up. Consider the climate that you're in. A cold floor in the middle of winter may not be a desirable sensation. Investigate the finishes and stains per product and request that your installer use safe adhesives or grout.
Lastly, purchasing locally made sustainable flooring products that reduce transportation emissions are always your best choice.