Several years ago I received a small Beech Plum from a friend in NJ. Living in the State of Washington, they are quite uncommon around here. In that I only have one, which is doing extremely well, I get no fruit. My question is about taking some cuttings so that I can get more that would hopefully help with pollination. From what I read, they aren't hard to start via cuttings. My question is whether that would solve my fruiting problem. Thanks!
No, this will not be a solution to your problem. From cuttings of the same parent, you will only create more stems that don't pollinate themselves well.
You need a genetically different (seedling, cuttings from a different parent tree) Beach Plum in order to achieve successful cross-pollination.