I would not get rid. Have you had plums in earlier years? Pruning needs to be done in July not in the winter. If you cut them back in winter it is possible you cut off the fruiting branches which I suspect led to the lack of flowers.

Plums flower very early too and lose them to bad weather before they are pollinated

That was my first thought too Pam but Raywat has had no flowers either which is why I wondered if she had pruned the tree at the wrong time.

Good point Scotsgran, I wonder how old the trees are......young ones often don't crop very well at the start

No plums here this year either, last year it was hundreds of plums but no apples at all, its the way it goes...

I had two plum trees, one in the back garden and one in the front garden. I took the one in the back down when I discovered it got no sun at flowering time due to a new build. They were both bi annual fruiting. Luckily they took turns to fruit. One, one year and the other the next. I regularly got over 70lbs of plums from them and was able to keep our village in plums. Sadly the 2nd tree has not been fruiting as well as it did. I have two apple trees which do the same.

.We have a Really old plum tree, something like Czar..poor thing, half of it blew down, its got woodworm in the trunk but there from the break is a new branch growing, it has plums but I noticed yesterday something like "shothole" on the leaves.....we have planted a victoria and a golden gage, these have only been in about three years and not fruiting yet but hopefully will before the poor old Czar finally peggs out.......

i prune in june july every year, this year the same.just no fruit,and my friend down the rd as never pruned hers at all, both got nothing this year. my trees about 9 or 10 yrs old

I think its probably the weather, very wet year and wet spring
Hope for better next year and look closelyto see if you get flower buds early.
Too late now but feeding them next spring could help the trees too

It sounds like you are doing all the right things. I'd take Pams advice.