This app was mentioned in 11 comments, with an average of 1.55 upvotes
Unfortunately, just like with Alexa, there are some fairly strict rules on choosing an invocation name. This page outlines the rules, and they don't allow single word invocation names (like 'Plex'), unless you need it for your business, which I'm guessing means you need to own the Trademark on that word.
I actually wrote a custom Alexa Skill for interfacing with Plex and stalled on it once I tried to publish it and realized I couldn't use 'Plex' as the invocation name, and that I'd have to use something completely unrelated and two words long, as well as the fact that I couldn't call the skill 'Voice Control for Plex' (the name of my Android app ) as Elan asked me not to use 'Plex' in the name of my skill so as to avoid confusion since they are working on their own Alexa skill. Sigh.
Not an API but you could just use my Android app, Voice Control for Plex. It supports Chromecast (IAP, but send me a PM and I'll send you a code).
I've been doing this for a year or two now using Voice Control for Plex with Tasker.
https://play.google.com/store/apps/details?id=com.atomjack.vcfp&hl=en
I use it via my Android Wear watch too.
ok if you can get access to a pc for her to use i believe you would have many more options here.
for example i use a program called voxcommando http://voxcommando.com/home/
its pretty easy to use and has limitless possibilities. I use it in conjunction with eventghost and tasker to have control in all sorts of different ways.
One thing you could definately use would be an IR blaster of some sort. I personally use a USBUIRT device that voxcommando and evenghost both have plugins for.
Using voxcommando with a usbuirt you can train the program with different remote codes and then just give that action a phrase to initiate it.
It also integrates wonderfully with kodi/xbmc for plex i just use an app called voice control for plex on android https://play.google.com/store/apps/details?id=com.atomjack.vcfp&hl=en
If you need to go the cheapest route and you already have a computer or laptop available just plug in the pc to the tv and grab voxcommando and a usbuirt. you can use the microphone on the android device with the voxcommando app called voxwav. Going this route would open up tons of doors for her to surf the web, type emails and other documents through dictation, get alerts, weather, change channels, volume, control lighting through external hubs like vera/hue/etc.
Ahhh I've been waiting for them to release the API, so I can integrate this into my app. In the meantime, you might try the Android app I've already written, Voice Control for Plex. It's pretty mature and fully featured (and includes Chromecast and Wear support). It's also open source.
Let me know if you'd like a code for Chromecast (it's an IAP).
https://play.google.com/store/apps/details?id=com.atomjack.vcfp&hl=en
This with Tasker installed. It adds a function to Tasker so you can use Autovoice to say "OK Google, watch the latest episode of the walking dead in the living room" etc
Not sure if this would work with the Fire TV as I don't have one, but if the Plex app for it responds to http calls like other Plex clients do, you could try my app out, Voice Control for Plex. If it works, it would at least make it easier for you to start watching a film :)
As for legal/copyright stuff, the only thing the Plex guys asked me to do was not to use the Plex logo. But if you have more questions, I'd suggest dropping Elan a line.
Since you use Plex, you might like my app, Voice Control for Plex. It's an alternate Plex client that uses voice input to trigger playback. It's free, with in app purchases for Chromecast ($0.99) and Android Wear ($2).
You can use Voice Control for Plex with Chromecast (https://play.google.com/store/apps/details?id=com.atomjack.vcfp) Google Now is supported with xposed I think.
Awesome! And if you use Plex, you might find my app of use :)
This isn't the best option, but it will do what you want:
https://play.google.com/store/apps/details?id=com.atomjack.vcfp&hl=en