Preheat the oven to 350°F (180 ℃) and lightly grease an 8-inch or 9-inch loaf pan.
In a small bowl, whisk the flaxseed and water together until thick and creamy. Set aside to gel up.
In a large bowl, thoroughly combine the flour, baking powder, rosemary, and salt.
To the flaxseed mixture, add the milk and olive oil.
Add the wet mixture to the dry and fold until about three-quarters of the dry ingredients are moistened. Add the walnuts, olives and tomatoes and fold just until the pieces are evenly distributed and the dry ingredients are moistened; the batter will be stiff and a little sticky.
Scrape the batter into the loaf pan and spread evenly. Bake until a toothpick inserted into the center comes out clean, about 35-45 minutes. Let cool in the pan on a rack for 5 to 10 minutes before unmolding to cool completely on the rack.