Is saying had had twice correct grammar?

Yse, in the right context; for example "She had had enough", "Henry had had bad reviews before" or "Bob explained that Keith had had a bad experience before coming to work for the firm". In these cases, the use of "had had" is the Past Perfect Tense of the verb "to have". One major use of this tense is to show that something began in the past and continued until another point in the past.