Yo Nicotanker - Howdy from Dublin - Ireland!! - we have great respect for the US service men and women - this side of the pond - tough job dude - take my hat off to you bro!!
In terms of Jazz, the one great thing is, that the old school drummers such as Buddy Rich, Gene Krupa, Joey Jones are still so relevant today - and of course more modern Dave wEckl for Latin/JAzz - super technique -
There's a few excellent resources online for general lessons - check out
» Free Drum Lessons - Learn How To Play Drums Online an excellent start for reading drum score, picking up the basics for all styles inc. Jazz - what level are you at? The secret to good Jazz besides timing is Rudiments - you have to nail these - not all 40 but certainly singles, doubles and paradidle family for sure! -
Basic tip -
Counting an 8 bar triplet in swing
One- trip-let, two trip-let, 3trip-let etc played on the bell
Kick and open hats on the quarter note (One, Two ec)
Snare played on the + (and) so + 1 tripl-let + 2 trip-let and so forth
Now play around with the snare on any of the trip-let-parts and you have basic swing. Hope tis helps dude Phil.