For the semi-transparent mirror (black), stick the darkening foil onto the acrylic sheet. Then cut out the same flower shape from the semi-transparent mirror and the normal mirror. Then cut out the frame in the shape of flowers from wood.

Apply wood glue to the edge of the normal mirror and place it in one of the wooden flower frames without a cutout. This completes the bottom layer. On top of this, glue another flower frame without a cutout. Three layers with a cutout follow. Make sure that the cutout is on top of each other. After that, another wooden frame without a cutout follows. Now apply wood glue to the edge of the semi-transparent mirror and attach it to the last wooden frame that is left.
Now glue the LED strip to the inside of the flower frame and optionally stabilize the solder joint between cable and LED strip with 2-component glue. Now the semi-transparent mirror can be glued on top.

For programming I have adapted the "strandtest" example of the NeoPixel library so that the rainbow function is called there.