re: I'm assuming the little box converts to the DC current an LED needs.
Usually how the bridge works there is four diodes and it is possible one or more are damaged.
As ET suggests I would pop the black box open and put a volt meter to work and tell us what outputs you get where... if you care to explore the thing further that is.
If you are getting AC at the output to the string this would answer a lot of questions.
You could also just live with the flicker if nothing else is wrong...like smoke or a extremely hot or loud transformer...
Maybe your reflects are just faster than most of us. It does happen that some folks see lights blinking with 60 Hz.