When I am Caribou hunting or Moose hunting I keep a piece of paper towel in the pan with the frizzen closed down tight on it, and keep it under my rain coat if it is raining. There is usually plenty of time to prime when the game is spotted.
Deer hunting is a different story. I dump the pan often and re prime immediately. I have hunted all day in the rain on many occasion and have never had any problems with ignition.
About thirty five years ago I was deer hunting in the rain all day, and at the end of the day my arm was so sore from keeping the lock up under my arm pit, when I hit the hiking trail at the top of the mountain I decided to head back. About half way down the mountain I decided to relax my arm and let the rifle get wet, the day was just about over anyway. Just about the time the lock got good and wet I met another hunter walking on the trail. In those days there were not many flintlock rifles in the woods, and he was surprised to see mine. He asked a lot of questions about it, including , "how reliable is the ignition". I told him, on a good dry day it was quit reliable, on a damp day it was not quite so reliable. He said " how about on a day like this." I told him that there was not a chance that it would fire now because it was so wet. At that he said "you mean you have been hunting all day with a rifle that will probably not go off, why would you do a thing like that. I thought for a minute and said, "beats the $#*! out of me, I guess I just like hunting with a flintlock rifle."