What flooring is mold resistant?
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For what area?
Vinyl or tile would be best, and your question is a bit troubling. Mold will grow anywhere if there is enough moisture. If you have a moisture problem, chances are you have a ventilation problem and may have mold in the walls you do not see and can make you very ill. I would have a consult with a licensed mold remediation company to see what can be done to fix the problem.
Mold can live on the back of vinyl tile. With ceramic tile and concrete you can wash with bleach to get rid of mold.