Well it is a question that should be asked. We're all quite used to Peter Jackson's lore escapades in the past yet this is quite an undertaking even for him. He's redefining a major(ish) character's back story and personality, with as only explanation the sentence "Do not speak to me of dragon fire ! I know it's wroth and ruin ! I have faced the great serpents of the north !". Well the first clue to be taken is that he apparently fought against the wyrms of the north. So the north as in northwards of mirkwood. As such he means the grey mountains, the remainder of the iron mountains, where Melkor bred the first drakes. So obviously there are dragons in the north of Mirkwood, it's from the grey mountains (the withered heath to be precise) that Smaug and (earlier on) Scatha came from. The question remains when and why did Thranduil fight the drakes ? Well, he might have been born during the first age but he never joined in the siege of Angbad with the noldor, he was born only slightly before the fall of Doriath and the sindarin certainly did not fight the war of wrath.. In the second age dragon's weren't very common, and the only record of Thranduin doing anything of note was the battle of Dagorlad in the last alliance. The only time he ever even was close to a dragon was after the attack on Erebor. So once again, PJ's doing what he wants, the explanation may come in the third film, but it probably won't.
But, we do have a (sort of) explanation, form IMDB, about Thranduil's scar, relating not to how he got them, but to how they appear and dissapear : Thrandiul’s sudden cars reflect a little emphasized of Tolkien’s lore: elves’ “Fëar” (a metaphysical concept analogous translatable as “soul”) occasionally influences the “Hröa” (the fleshly, physical body), particularly under moments of extreme stress. This can manifest as extreme physical changes that reflect the mind’s state, in this case deep war scars.
- The mad Hobbit
- The mad Hobbit