Q: Is it appropriate to chant the Litany of Loretto during mass and if so, when and at what part of mass? Or is it used for private devotion except at the shrine at Loretto and at certain churches in Rome?
A: In general, no, the Mass does not have a place for the Litany of Loretto, as beautiful as it is. The US Bishops included it in their book Catholic Household Blessings & Prayers, making it especially suitable for people to use at home. It could also be fittingly included in devotions to Our Lady at church.
I’m sure that there are people who incorporate it into Mass, either after the homily or after communion. I advise against it because I like to protect the integrity of the parts of the Mass.
By all means, pray the litany. But do it before Mass, after Mass, in a devotion at church, or as part of prayer at home.