(Forgive the crude test mounting to the cardboard box...I haven't decided where I'm mounting my handful of Dots...)
The screw hole is designed for #6 screws with a head <7mm in diameter and <3mm depth. If the screw head doesn't fit into the hole flush then the Dot won't snap into the clips. I recommend using anchors (mollies) if you are mounting into drywall.
You can basically lay the clips onto the Dot while upside-down and figure out the mounting pattern/distance.
You can use between 3-6+ of these clips depending on your mounting needs. It has not been tested in under-mount scenario (i.e. hanging from a horizontal surface). I claim zero liability for your Echo Dot in what you attempt to do with these clips. Use at your own risk ;-)
Please provide feedback if you decide to give these a try.
I printed a set of 4 clips using PLA at 218-C and a 50-C bed (optional if you have it) and it took less than 30 minutes. 0.4mm nozzle.
Print and Go
Nothing to do after you print. They come off the bed clean and ready to use!
This was created directly in Blender 2.79c after first doing a crude model of the Echo Dot itself. At first I was going to create my own flavor of the one-piece mounting solution, but then decided to see how a small clip would work. Looks like this is the first of its kind here on Thingiverse (correct me if I'm wrong).