...had started writing after she had watched the film.

Grammatically correct.

No need to repeat the "had" in the sentence.

Mary said that she started writing a story after she had watched the film.

Mary said that she had started writing a story after she watched the film.

I withdraw my earlier answer. Punkey is right. We use the past perfect (verb 'to have' + past participle) e.g. 'had started' when a past event or action occurred before another event or action. I had started to walk to work before the rain began to fall.

Thanks to both of you.