Free Shipping for Some Products

I’m having trouble figuring out a shipping issue that seems like it should be straightforward….

My company ships physical products. Most of them have Flat Rate shipping using the Table Rates plugin. However, a handful have free shipping. I cannot figure out how to exclude the free items from the flat rate charges. Seems like I should be using shipping classes for this but once I add a class, I can see how to put a product in it but not how to associate a shipping method/cost with the class.

What am I missing?

Thanks!