How to blink next button of storyline player when the timeline end of the slide.

Three things:

1. You don't have to write a trigger to hide a layer when its timeline ends. In layer properties, there is an option to do that.

2. The timeline on the base only ends once, so it can be used to start the sequence, but not to continue it. You may need two layers.

3. I'd have to see the project to know for sure, but you might have it set up right, except that layers default to Automatically decide the state when revisited, and they may be deciding to use the saved state. if so, it might work if you set them to Use initial state on revisit.

With all that said, here's a sample that seems to do what you are asking.