IMO, the only reason to patent, copyright or trademark is to protect commercial value. With flies that's very difficult to do, since as has been mentioned, proving originality would be difficult. Besides, with today's myriad of materials, most any pattern can be changed slightly, still look & in most cases perform the same, and not infringe on the legalities.
There was a gentleman by the name of Bob John's, a noted tier who patented & trademarked fly patterns & names, and frankly I'm betting he didn't get rich from the process. I have a couple of his flies, still in the package. There are many patterns listed in books & online that are very similar.
Again, IMO, there is a big reason NOT to want to patent, trademark or copyright an original pattern, if a tier wishes to be well known. No one gets much publicity from fly patterns no one knows about, cannot copy or cannot tie. The big name tiers all trademark their name, not their flies. They want their patterns to be in wide spread use & want everyone to know who they are, even those of us who tie. That's where the money is in tying. Notoriety.
Take the "Clouser Minnow" as a good example. It may be the most widely tied & used fly in existence today, and everyone knows who originated it. Bob Clouser certainly sells his fly, but so does everyone else. "Clouser" used to be a trademark, but I'm not sure who holds the trademark. Using the name by anyone other than the trademark holder is the legal issue, not tying & selling the fly. But, again, everyone knows that Bob Clouser originated that fly, and even his name has become synonymous with that pattern. That's what a tier wants to be "famous" & that's what gives commercial value to what a tier does!