Which red pepper to use?
Most recipes I've seen for clam chowder suggest adding salt and black (or white) pepper to taste before serving along with a sprinkling of chopped/minced parsley leaves (either in with the clams or as a garnish).  A touch of white pepper in cream-based dishes can be a wonderful addition.  

I have never seen a recipe for clam chowder that includes cayenne pepper or pepper flakes - I would think the heat in either choice would work against the delicate flavors of the clam and cream (and even if you were making the Manhattan version with tomatoes, that dish is typically briny and savory - not what I'd call spicy).  

Is it possible that the recipe could be referring to paprika?  If that's the case, a little bit of mild paprika used as a garnish on top when you serve the clam chowder should be fine, but remember that a little of that can go a long way in a delicately flavored dish.