Suggestions on where to go for custom mudflaps?

I know Kinko's will print banners with your artwork. The trick is making SURE the ink will adhere and dry to your substrate. They likely have their ink dialed in for the banner material.

I spent a couple of decades in the printing industry. Printing on plastic or rubber can be tricky, the ink has to have an electrical charge compatible with the surface you print on. Get it wrong and you get poor coverage or ink that takes forever to dry. Worst case scenario you have ink that never dries and ends up smearing.

Sublimation makes vibrant colors that will last forever, but the substrate has to be able to withstand heat and pressure during the color transfer. Sublimation will also require a minimum order of artwork in powder form on nonstick paper. Under heat and pressure the powder becomes a gas that embeds itself in fibers or plastics. It won't wash off.