Do flavors remain on an enameled skillet? A simple test to determine whether particles from cooking remain in the skillet and get absorbed by a subsequent meal is to cook fish (or something particularly spicy) and then wash the pan carefully. If you can detect that flavor in the next dish, some kind of leaching is going on.

After many years of using tri-ply, I can confirm that I've never detected this pan-to-dish flavor exchange to occur. I've burnt food on stainless steel many times, and when that happens it takes a lot of scrubbing with Bar Keepers Friend to get the carbonized food out, but the pot comes out as good as new. The trouble with tri-ply is that the bottom of pots remain perfectly flat, but skillets warp, making them tiresome to use on ceramic stoves.

I'm contemplating a new type of cookware. Given the uncertainty of whether a cast-iron skillet's seasoning makes it into the food, I'm skipping this type of cookware. Instead, I am looking into enameled cast iron. 

I'd like to focus on just the flavor. If we assume that the cook cares for the enamel so it doesn't chip or similar, will there be flavor transfer between dishes?
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."