Mine is an unpainted black plastic, but it has unfortunately received alot of scratches and scuffs/discolorations over the years, it seems.
I don't believe that these were painted, and from what I can tell of the remaining surface condition on my 82 LS, it isn't a flat or matte black either, just perhaps a bit less shiny than a high gloss. It is smooth (aside from the scratches) - you might find a flat black paint to try to use over the gloss - but I don't think that it is a bad look on your bike either.
Some other folks here have much more automotive painting experience who will probably chime in soon on paint suggestions. These cowls are available still - but are very pricey if ordered new from a dealer. You can keep an eye out for one on ebay, etc. - just be aware of the tendency for the tabs to break on the edges and that not all ebay sellers are aware that there are supposed to be tabs.
It looks as if the exhaust pipes on your bike were also painted with a somewhat glossy type paint - do you know what was used on them ? I have touched up my exhaust with
the POR-15 Black Velvet high temp paint - it is very "flat" and doesn't have any shine to it at all - I think that your exhaust system color looks somewhat better.
P.S - After looking at your silver wheels, I am thinking of possibly getting my wheels repainted in silver - mine still sport the flaking, yellowed- white original enamel at this point !