I doubt it would work for Kodi, only amazon and netflix right? And even then you’d need the remote to put in the parental control code wouldn’t you?
Unfortunately I don’t use the two things you mentioned - Kodi and parental controls. I primarily use Amazon, Netflix and now the Firefox app to access YouTube. Even if Alexa hasn’t worked on a specific app (i.e. it doesn’t find YouTube inside Firefox), the voice control to pause, play, etc…works through the Echo once the content is playing.
So for me I really did just add the Fire TV to my Alexa app and was good to go.
I hope others can help answer this since I plan to install Kodi at some point.