1. Open Alexa App
Here are the download links if you do not have it installed.
2. On the bottom, select the Devices tab
3. You should now see “Echo & Alexa” at the top. Select that.
4. There should now be a list of all the things connected to Alexa through your Amazon account. Select the name of your Echo Dot.
5. Scroll all the way to the bottom and select About
6. You will now see your MAC Address of your Echo.