How do your rid cinderblock walls of mold and can you paint walls afterwards to prevent more mold?

Bleach is what kills mold. Cinderblock is so porous that you will be scrub brushing forever, but unless you hire a pressure washer and a moon suit and make a huge mess, that is what you have to do.

Paint isn't going to stop or prevent mold and will most likely peel off anyway. You have to find the source and fix it, and also prevent it with proper air flow, cross ventilation, heat, and dehumidifiers. (I have read however that dehumidifiers just pull moisture right through the wall from outside.)

I agree with joy, you have to remove what's causing/allowing the mold to grow. Bleach is good on a solid surface but there are better products for something as porous as cement block. I have used Mold Blaster and also biocide, some actually have you add a cup of bleach to them. After its dried abd ventilated for several dry days you can prime with Kilz and use a block filler.