I found this source
but i don't know whether it is what you are after.
Thranduil’s sudden scars 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.
Source Edit : I have also found this reference which seems to state that Tolkien made no reference to the Scars on Thranduil's face in the books.
Thranduil's scars are decidedly non-canon.
According to Tolkien's texts, the last battle Thranduil saw (up to setting in
The Hobbit) was that of the last alliance at the end of The Second Age.
However, in the 1900's of the Third Age, according to text, the "serpents of the north" were fought and mostly slain.
In all likelihood, Peter Jackson is taking creative liberty with the story.
On a more symbolic note, the scars could represent the pain Thranduil has endured in war (he watched his father die in the battle of the last alliance).
Source
scifi.stackexchange.com/users/25406/GeoffWilson
This is discussed in the Director's commentary.
Thranduil's prior encounter with dragons (which the Director happily admits is not from the books) was included to explain his deep isolationism and the reason why he wouldn't help the dwarves.
There's also the suggestion that a firedrake killed his wife, explaining her absence from the film.
As to the sudden appearance of his scars, the implication is that he normally uses Elven magic to disguise them.
To emphasise his little speech, he allows this 'glamour' to drop momentarily.
Peter Jackson:
What's interesting is that Thranduil's had this encounter with dragons before ... and his wife was ... Boyens:
There's a conceit we came up with.
Actors need that.
They need to feed on that backstory.
Where did this isolationism come from?
I also like the notion that this very 'closed off'
character is also oneof the greatest fighters on Middle Earth.
scifi.stackexchange.com/users/20774/Valorum
Thranduil mentions that (Paraphrasing because of memory) "Do not talk to me of Dragon Fire
, I have felt is wrath and ruin.
I have faced the Serpents of the North".
Although I don't think Tolkien made any canon mention of these fights, or none that I've found.
I think Peter Jackson did this to add some common ground between Thranduil and the Dwarves that I'm sure will play some part in the third film.
scifi.stackexchange.com/users/25416/Tommy
I read the Silmarillion many years ago, and I immediately assumed, when Thranduil mentioned the serpents of the north, that PJ concocted a history where Thranduil had a run-in with one of the dragons from Angband somewhere in the First Age, when he still lived in Doriath.
It is plausible.
I did not think the scars were real; I thought he summoned the memory of the wound
and it manifested on his face briefly.
But I really think the 'scar' was the illusion, not the reality as so many others think.
scifi.stackexchange.com/users/35296/Edriel
The book does not refer to any scar or to Thranduil being somehow disabled, but the movie makes it seem so ´cause the Movie!Thranduil has an extensive scar and an apparently blind eye as a result of the scarring (caused by the dragon fire).
What does it mean in the movie?
I dunno, I was baffled, too.
But I understand it in two ways:
he battled the dragon, it scarred Thranduil for life, and now he is forced to wear a glamour on his face to hide the ugly mark.
But it probably reveals itself after a period of stress or in times of anger.
he battled the dragon, it scarred Thranduil for some time, and the resulting mark on his face really did look like this for an unspecific long period of time.
However, the scar got already healed somewhere in the past, and now, when it revealed itself again, it must be just a manifestation of the venomous anger that Thranduil holds inside of him.
scifi.stackexchange.com/users/43273/Calucifer13
My guess is that PJ took the fear/hroa concept one step further to expose the hubris of Elven arrogance/beauty.
Translation:
dragon's fire is the one thing elves cannot fully heal and scars permanently.
scifi.stackexchange.com/users/32741/Rob
In the heated discussion between Thranduil and Thorin, for a moment, Thranduil's face suddenly turned very deeply scarred & wounded and then immediately returned to normal. What was this about? Is it a reference to anything that was cut out of the movies? (I have not read the books, sadly, but am very curious about this.)
What exactly happened to Thranduil's face while he was arguing with Thorin?
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<tolkiens-legendarium><the-hobbit><desolation-of-smaug>
scifi.stackexchange.com/questions/54780
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Thranduil’s sudden scars reflect elves’  “Fëar”. The implication is that he normally uses Elven magic to disguise the scars. In the film, this may have been to add some common ground between Thranduil and the Dwarves. Thranduil shows Thorin his scars to prove his point during the argument and to show he has common ground with the Dwarves. 
Thranduil shows Thorin his scars to prove his point during the argument and to show he has common ground with the Dwarves. 