How to save a shared video to my Camera Roll on iOS?
Apple doesn't have a solution on iOS to accomplish this. I've not found any third party app from the App Store that will read the shared stream videos or receive a paste event (you can copy the video from Photos app on iOS, but pasting it anywhere seems to not work for me on iOS 8.x)

I use iPhoto on OS X to view the shared video and then import them into my library. From there, I can get the videos onto iOS. Not exactly your preferred solution, but it works well enough for me.