Preheat oven to 350°F (175°C). Line a 12-cup muffin tin with liners or grease well.
Mix in a medium bowl, the flour, ground flaxseed, baking powder, baking soda, and salt. Set aside
In a larger separate bowl, stir together the lemon zest and granulated sugar until fragrant. Whisk in eggs until slightly pale. Blend in the oil, yogurt, milk, lemon juice, and vanilla until smooth.
Add dry ingredients to the wet and fold gently until almost combined. Toss berries with 1 tablespoon flour, then fold into the batter carefully. Be careful not to overmix.
Divide batter evenly among muffin cups (about ¾ full). Bake 22–24 minutes, until a toothpick inserted comes out clean. Let cool in the pan for 5 minutes, then transfer to a rack.