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.
These are more like a healthy snack than a dessert. It's fun to give people a dandelion cookie because people get all weird about eating a weed. Be sure to gather unsprayed dandelions and use only the yellow petals; the green part is bitter.
I use an ungreased Calphalon cookie sheet. The cookies will stick to the pan slightly, but they're easier to remove when cooled. You can use egg instead of flaxseed, and milk instead of chia seed and water. To get fluffier cookies, use less oats, more flour, add 1/2 teaspoon baking powder and cut in 2 teaspoons butter. I use steel-cut oats; rolled oats will yield a softer texture.