Hi Mike.
I've been working on this arrangement by Kirk for a few weeks now - and having a lot of fun too - and this
slide stumped me for a little too.
I think I have it pretty down pat now so I'll see if I can explain how I do it - though keep in mind this may not be entirely
correct ... I'm a 10 month guitar newbie.
The first slide I do is in the 7th measure where I use my index finger on the 2nd fret of the 4th (D) string (note = E) and slide up to the 4th fret of the same string (note = F#). Basically, strike the 4th string for the open D note first, then fret the string at the 2nd fret and strike the string again, then for the F# just slide up to it. The existing vibration in the string should allow you to hear the F# note when you slide up to it. Note, this same slide occurs in the 14th measure too.
The next slide I do comes in the 15th fret. This one is the one I have most trouble with. This is where we strike the open D string first followed by the open G (3rd) string. The next note (F#), which is the 4th fret of the D string, I actually slide up to. The way in which I do this (I think) is to strike the open D string but VERY QUICKLY hammer on to the first fret (with my middle finger) then slide up to the 4th fret. Note that this is done very quickly. Seems to sound correct for me. I also do this same slide in measure 26. Also, by using the middle finger this allows me to use the index finger for the B (2nd) string, 3rd fret that follows.
Anyhoo, I hope this helps, but keep in mind that this is just my take on it ... not entirely sure how
correct it is.