This might have been mentioned before, however I'll just post it as both a guide as well as a request for a proper app. The method described below is basically a crude way of getting things done, but hey, it works!
I have managed to stream my phone screen (Note 3) to my tablet (Note 10.1) using AirDroid. I was pleasantly surprised that it worked.
Here are the steps:
1. Install and start AirDroid on both devices (root required)
2. Use one device to connect to another using your favourite browser (I used Chrome)
3. Select screenshot on the device being streamed to
4. Pinch-to-zoom to fill the entire screen
5. Rotate the screen if it is in the wrong orientation (Chrome works better)
6. There you have it...
There is a slight lag of around 2-3 seconds so if you can live with that, that's fine. If not, wanna write a program for this?