I admit that I don’t know much about Echo but based on the tutorial you link to you don’t need my.openhab or to write some bridge at all. The purpose of my.openhab is to expose your openHAB to IFTTT and clients that are external to your LAN without the knowledge of how to open up a port in your firewall or setting up a secure connection (e.g. VPN).
Since your Echo is on the same LAN as your openHAB, there is no need for this, Echo can talk to openHAB directly through the native REST API as documented here. If your openhab.cfg is configured for security=external you don’t even need to supply a username and password.
If I’m reading the tutorial correctly, you just need to use the LAN IP address of your openHAB instance in the onURL or offURL JSON config you send to the Echo and you should be good to go. It really is as easy as that and there is no need for my.openhab in the mix.
You might also be interested this thread and this thread which is related to VoiceCommand.
Rich