Preheat oven to 350 degrees F (175 degrees C). Lightly grease a baking sheet or line with parchment paper.
Combine flour, oats, brown sugar, flax, chia seeds, and dandelion petals in a bowl. Crush lavender flowers with fingers; add to flour mixture. Stir in vanilla extract and enough water to create a moist dough that holds together when squeezed. Portion dough into 6 cookies and arrange on prepared baking sheet.
Bake in preheated oven until cookies are dry and fragrant, about 10 minutes. Allow to cool before removing from baking sheet.