Vacuum the dust and chalk. Clean water with a lint free rag for spills. I'm not sure you will be able to get any stains out but in my experience the cloth is still playable after cleaning with water. Don't drown the table
"Coker Tire Company offers several authentic Model A tires in both blackwall and whitewall styles"
https://www.cokertire.com/tires/styles/model-a-ford-tires.html
Choose a different analogy Glen ;)