The Alexa capability is not available for the original Fire Stick/box, it is only available with the subsequent newer devices.
This is not true. All FireTVs and FireSticks were upgraded automatically to FireTV OS 5.0.5 back in February/early March. This Update included all of the Alexa features that the 2nd generation FireTVs have. I have two first gen and one second gen FireTV and all have identical Alexa capabilities. They can basically do anything the Echo can accept for setting timers/alarms but they require a button press on the voice remote.
http://www.aftvnews.com/fire-tv-software-update-5-0-5-begins-rolling-out-to-1st-gen-devices/Before you can expect the Echo to natively control the FireTV, I would expect the voice features on the FireTV to need to be upgraded from simple voice search functionality to voice control. Right now, you cannot tell the FireTV to play a specific movie even with its own voice remote. You have to say the name of the movie, select the text that corresponds with what you have said, then select the proper movie/app from the choices that appear, and then start it. You cannot start something, pause it, exit, FF, RW, turn on closed captions, or any other such functionality via voice control, so to expect an independent device to be able to do so is unrealistic. However, once the FireTV is capable of such automation, then it probably won't be too hard for the Echo to integrate with it and take over control via voice without the need for the remote.
A Harmony Hub can integrate with Echo. This would give you the ability to tell Echo (through IFTTT or SmartThings) to "Trigger Watch TV" and it will turn on all the needed devices, set the appropriate inputs, and such so your FireTV is ready to use. Conversely, you can tell it to "Trigger Turn Off TV" and it will turn off all the associated devices. However, you still cannot easily tell it to start a specific movie, turn the volume up or down, FF, Pause, Play, Rewind, Exit, etc.