They do contain gluten however some claim that oats that are grown and processed seperately from any other gluten containing grains MAY be safe for gluten intollerant people.
If you stick to Sally’s book you don’t need to try to figure out an inflammatory index of foods. Her book points out that eating real food is really quite basic once you understand what traditional foods are and how to prepare them. Indexes and food pyramids are not based on good and truthful science.