What is the bicycle Danny MacAskill uses in his "Way Back Home" video?
He rides a prototype trials bike by Inspired Bicycles that will be called 'Skye' when it comes out.

Full details on his rig:

http://www.inspiredbicycles.com/danny_macaskill_r3.php

Inspired sell frames that you can build up to your own specification, useful if you already have a bike that isn't quite up to the job as you can move the parts across and go from there. They also sell complete bikes.

I am sure someone can correct me on this, however, the mainstream brands do not really create anything that comes near to what you get with an Inspired trials bike. There are other brands, e.g. Mission, you may want to see what your nearest LBS has, chances are that they may have someone working there that knows their stuff and has passion for it.

For now it would not do any harm to email Inspired Bicycles to see when the 'Skye' frame/bike is out and find out how much it is likely to cost.