I first heard this tale in... maybe 1999? It might have been part of the general paranoia about Y2K, though it could just as easily have been general ridiculousness, given that I heard it on the Art Bell show. (I wasn't listening by choice; my SO at the time liked to listen to the show for a laugh. In my opinion, the level of ignorance was simply too painful for laughter.)
It was less organized, and good old Art had fewer details, but the gist was the same. The contrails lasted too long and "didn't look normal". Just after one particularly odd-looking and long-lasting contrail appeared over his house, his entire family caught some sort of strange flu-like illness. The military is obviously experimenting with germ warfare!
Why this couldn't have been actual flu that one family member gave to the rest, I don't know -- he pretty much dismissed that possibility, unsurprisingly. And if you're testing wind vectors, the feasibility of such a delivery system, etc., by using something relatively harmless, which is what he claimed, then there would have been no way for anyone to find out how well the system had worked. Few people will go to the doctor with a minor illness, so how would they even track where the germs went in any reliable fashion?
Not that logic was ever much a part of the show. This is the same man who found hints of deep conspiracy in the lyrics to "These Boots are Made for Walking".