There's evidence that Thranduil may have lived in, and have been a survivor of, Doriath in the First Age. The original long entry for SA750, given in HoME 12, reads:
Remnants of the Telerian Elves (of Doriath in ancient Beleriand) establish realms in the woodlands far eastward ... The chief of these were Thranduil...
Naturally the timeline was subsequently altered, but it's unclear if Thranduil's past was lost owing to compression (a point which CT touches on in his commentary) or rejection.
If we accept compression, then following the Ruin of Doriath he would have been part of the Elven colony at the Mouths of Sirion and/or on Balar, and would have seen dragons in the War of Wrath.
Update - 2nd November 2014 - in the commentary to the extended edition, Jackson begins saying "Thranduil's had this encounter with dragons before, his wife was..." before being cut off. It's also remarked that this was "a conceit we came up with, because actors need that to feed on, a backstory". Obviously we don't have this backstory expressed explicitly in the movie itself, but that's evidence that it does exist.
Update - 17th December 2014 - in the third movie, the "his wife was..." comment is made clearer. Thranduil's wife was killed at Gundabad, which comes up in a conversation between Legolas and Tauriel. There is however no mention of the manner of her death, but we can deduce from combining this with the DoS extended edition commentary that dragons were involved.