It sure sounds like a phase shifter, but I'm thinking he's going through an effects box I know Roland makes a modeling effects box for acoustic guitar - there may be some stomp boxes that could produce that effect - there are so many out there? Could also be like a computer - Guitar Rig or one of those. Sounds like the treble is pulled down to get the nylon sound (which could also be part of the effect) and you can hear him damping the strings pretty hard with the palm of his hand, probably to keep the effects from being too pronounced as it sounds like he has a lot of the effect going on and it seems to feedback and battle with the rhythm of his picking at times.

Pete Gallatin
http://www.reverbnation.com/patiopete