Preheat and over to 350° F (175° C).
Crumble approximately 1.5 teaspoons of the flowers between your fingers or with a mortar and pestle (reserve the rest, and preferably the nicest looking ones for decorating the cookie tops). You can remove the thin stems if you have trouble crumbling them up, but they're perfectly edible.
Combine the flour, crushed flowers, and baking powder. Stir/sift together and set aside.
Using a hand or stand mixer, combine the butter and sugar until they're well mixed.
Add the vinegar and almond extract to the butter and sugar, and mix well.
Add the flour mixture a little at a time, and continue to mix until well-combined.
Form the dough into small circles and flatten into patties by hand or, for a more uniform appearance, by pressing them into circular cookie cutters.
Gently press a preserved cherry blossom into the center of each cookie. try to make sure that they're completely pressed into the dough and not sticking out at the edges, or they may burn.
Space the cookies out by about 5-7 cm (2-3 inches) on a cookie-sheet. Bake for 10-15 minutes, or until the bottoms are a very light brown. Baking time can vary depending on your oven and the colour/material of your baking sheet, so keep a close eye on the cookies.
Set the finished cookies aside to cool on the tray. They'll be fairly soft right out of the oven, so make sure not to disturb them until they've cooled off completely.