This is the only NEC-approved kit I know of:
http://s667.photobucket.com/albums/vv33/royvegas/?action=view¤t=TheEliminatorTurbografxCleaningKit.jpg&sort=ascending(Thanks Roy!)
Doc's, Performance, and High Frequency each made one or more multi-system kits that including cards for the Grafx/Express. There's even one on ebay right now, but all of those hard plastic cards for console cleaning are really just the same thing cut to different sizes. Most any card from an old Genesis/SNES/SMS cleaning kit will work as long as it's straight and doesn't have some damn handle attached.
That said, Necro is right - your console probably doesn't need cleaning. Everything else may die on our systems, but we Turbo owners are lucky in that one respect. Clean your Hueys on your pants' leg, or, if you really want to go balls out, with q-tips and the highest percent isopropyl you can find and you should be good. I've only ever needed to clean the hucard slots on those crappy converters that tarnish easily. One time I cleaned my Supergrafx because that thing acts as a dust funnel and it wasn't loading one time in ten. Otherwise, hucard slots are golden.
Here's a pic. Look at these stupid things. The Genesis one fits the TG16 perfectly and the Turbogrfax one is too small!