Don't try to clean them! Mold is very hard to kill completely and can be a health hazard.
I would keep track of all conversations you have with the company - dates, times, person you spoke with, etc. First line of attack is to have Visa dispute the charge. If there are problems with that, contact the Better Business Bureau and your state's attorney general.
If they sold the product as new and it clearly is not, then it is fraud. It's possible that it's just a mixup and the chairs were sitting in a warehouse for a long time and got damaged, but regardless you should not accept them and the company should work with you to either refund your money or send you new product. If they are unresponsive, the BBB and attorney general are the way to go, especially if it turns out that there are lots of complaints like yours.