Hello,
This does not address the risk of cc through the slicer but here is the FAQ from the Black Bear Deli meats website:

Q: Are Black Bear products gluten free?

A: Nearly all Black Bear Meats are gluten free except: Rotisserie Style Chicken, Lite Franks, Lite Beef Franks. All the rest of our products are free of wheat, rye, barley and oat proteins.