Whisk flour and salt together in a medium bowl and set aside.

Cream butter and sugar together in the bowl of stand mixer on medium speed until light and fluffy, about 4 minutes. Add vanilla extract and mix to combine. Slowly add flour and mix on low speed until a dough comes together.

Turn dough out onto a lightly floured surface and shape into 2 flat disks. Wrap each in plastic wrap and chill for 30 minutes.

Line 3 baking sheets with parchment paper. Roll out one of the chilled dough rounds to 1/4-inch thickness and cut out flowers using cookie cutters of your choice. Re-roll the dough up to 3 times and continue cutting out cookies. Transfer cookies to a baking sheet using a flat spatula. Place cookies about 1 inch apart, fitting about 12 on each sheet.

Roll out the second dough round and repeat cutting out flowers until you have about 3 dozen cookies in total. Freeze cookies for 20 minutes to help maintain their shape.

Preheat the oven to 350 degrees F (175 degrees C).

Bake until the edges start to look pale golden, 10 to 15 minutes. Cool on pans for 5 minutes. Transfer to a wire rack and cool to room temperature, at least 1 hour.

Combine confectioners' sugar, 5 tablespoons water, and meringue powder in the bowl of a stand mixer and mix on medium until a thick icing forms. Add more water, 1 tablespoon at a time, until desired texture is reached. Divide icing among several bowls and tint with desired gel food coloring.

Decorate cookies as desired using a pastry bags and tips. Reserve any leftover icing in an airtight container for attaching the sticks. Let icing dry, 4 hours to overnight.

Attach lollipop sticks to the back of the dry cookies with royal icing. Tie together with ribbon or arrange in a gift box.