It would have been a lot easier if you mentioned which instances in the song had that technique with reference to the tab.
But I've found the tab you're referring to:
http://www.songsterr.com/a/wsa/sungh...-tab-s268648t0
What Sungha and Rafferty do is basically an emphasised palm muted downward strike on the string being played creating a click/slap sound in conjunction with the bass note.
However, I find that more often than not, especially on the 6th string, the note is not even heard, just a slap. Alternatives you can do to get a cleaner sounding note with the intended percussion would be:
X5X:
1) Mute the 6th string (and 4th too if you can or need to) with available fingers and turn your right thumb 45 degrees clockwise (so that your thumb is pointing towards the treble side) and do a bass slap (swift flick of the wrist and recoil) on the 6th/5th(4th) strings
2) Hammer on the 5th string with your left hand while you use your right hand to just slap the 6th string
5XX:
1) Same as above except muting the 5th(4th) string(s) instead, and rotating your thumb anti-clockwise in this case might be more appropriate as it is the protruding part of your thumb contacting the intended string which causes the note to ring out
2) Same as above except hammer on the 6th string with left hand while right hand slaps the 5th(4th) string(s)