As seomeone mentioned above, use the Infuse app to airdrop movies from the device with larger storage to the one with smaller storage, and then delete it as soon as you've watched it.
Its not streaming it, but it solves the problem of lots of files on one device with lots of storage, and little space on another device. The airdrop transfer is very quick as well, a few seconds for a typical TV show, no more than 10-20 seconds for a movie.
This is what I do pretty much on a daily basis for my commute.