Is writing a diary good for your memory?

I sincerely doubt that. Memory is pretty much fixed. Memory can get worse if you don't take good care of yourself, however, and if you do take good care of yourself, it could be at its peak. So it is somewhat malleable. The amount of stress or distractions in your daily life can also have an effect, but they don't really affect memory as much as they affect memories, if we consider memory a psychological function and memories as elements of what we remember. And that's an important difference with an distinction.

Keeping a diary or journaling can do two positive things, but neither of them really have anything to do with improving one's memory.

Writing something down helps you remember it. It's one more reminder of something, and if you come across that at a later date, it can remind you then as well.

Writing your thoughts down has a tendency to help you organize your thoughts, and that can become habitual, which is a very good thing. That, to me, is the real value of journaling. That's not something that helps you remember what's going on. It's something that helps you understand what's going on better.