Good call on the flask top. Couldnt figure out what kind of top would be made from silver, a flask would make sense. I believe that it is a "w" on it and the monogram would go along with a flask top. Good thinking.
Yes, I am sure there were silver matcholders for the gents. And many other things that it could be. Now comes the task of looking at web pics to look up each guess.
"P" is the 16th letter of the alphabet. That looks like a "16" to me. 16 stand for P, which stands for Pepper.
That's a Pepper shaker??
How's that for an overactive imagination? ?
I'm guessing its from a cosmetic of some sort. I found a metal lipstick tube before. go back to that area if you can, the other part is probably still there nearby. I found both halves of mine about 10 feet apart, probably hit by a mower at some point.
I'm thinking it's the top of something like a talcum powder container or suchlike, the type you would find in an expensive toiletries kit for traveling. A personal monogram on those pieces would not be unusual.