He probably doesn't have any siblings

If I'm correct it hasn't been stated that he has siblings.

I don’t believe he does.

I know in the movies that Tauriel is like his adopted sister but it doesn’t mention any siblings in the books

Yes I think you are right, but in the books, there's nothing.

Siblings of Legolas are never mentioned in the books, and so definitely not the films.

I am not sure because it has been mentioned nowhere.

Well they were never mentioned if they exist, and I think if there was a sibling they'd likely get a line or two in the Hobbit movies (since it has so many changes against the books, and since Legolas is in that movie). But I guess it's possible...