Do flavors remain on an enameled skillet?
Enamel is a very hard-wearing, non-porous surface. It's very similar to the glaze on porcelain. A well-washed mug doesn't make your tea taste of coffee. 

As a more personal example, we've got a couple of enameled cast iron dishes. While we mostly use them for quite strongly flavoured foods we don't hesitate to use them for more delicate foods as well. They go through the dishwasher in between. Here's what one well-known manufacturer says (among other things): "vitreous enamel surface is impermeable and therefore ideal for raw or cooked food storage, and for marinating with acidic ingredients such as wine."