Never use harsh chemicals to clean painted furniture. This includes furniture painted with chalk paint, traditional paint (aka latex paint), or any type of paint.
Regardless of the sealer used (i.e., poly or wax), furniture cleaners can potentially damage topcoats.
“– Vinegar (apple cider or white vinegar) – Degreaser that has not been diluted – Hydrogen Peroxide – Bleach – Mineral Spirits