This app was mentioned in 6 comments, with an average of 0.83 upvotes
try Cast Controller: (disclaimer: I made that app)
https://play.google.com/store/apps/details?id=at.xtools.castcontroller.android http://castcontroller.xtools.at
works with my own app too�� https://play.google.com/store/apps/details?id=at.xtools.castcontroller.android
Try this, it gets almost every video from the web on your fire tv: https://play.google.com/store/apps/details?id=at.xtools.castcontroller.android (full disclaimer : that's my app)
Have you tried Cast Controller? https://play.google.com/store/apps/details?id=at.xtools.castcontroller.android