four2109, White Cloud customer support tells me Flings use Lithium Ion batteries, "which contain no acid", and that this substance is most likely just adhesive used to attach the plastic cover over the battery. I'm honestly not entirely convinced. I've saved the Fling in question and will test some of the substance with a pH strip. If it's near neutral pH maybe I'll relax, but if it is acid I plan to investigate further. It is definitely a powder that has hardened, but it's easily broken apart. I absolutely believe I could have inhaled whatever it is if I'd puffed harder. And I am VERY suspicious of the other Fling that draws very hard. I may disassemble it to see if it's similar.
Customer service gave me a 10% off coupon. (I had requested a replacement of this one and the one hard-to-draw, which would have been 20% of a 10 Fling order.) They encouraged me to return any that don't draw easily, and they'd replace those, too. They wouldn't pay the postage to do that, of course. I'm more inclined to do some testing on them, just to satisfy my own fears/curiosity. I think that's worth the $3 minus postage that a replacement Fling would cost.
(update: they did mail me free replacements for both Flings, so I didn't have to pay any shipping.)
Here is a picture of the one that wouldn't draw, along with a "normal" one for comparison. You all can be the judge.... I'll post results from the pH test when I find my test strips.